When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be op...When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.展开更多
In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional d...In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.展开更多
In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently...In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently, Lassere [1] considered a scalar programming problem and showed that if the convexity of the constraint functions is replaced by the convexity of the feasible set, this crucial feature of convex programming can still be preserved. In this paper, we generalize his results by making them applicable to vector optimization problems (VOP) over cones. We consider the minimization of a cone-convex function over a convex feasible set described by cone constraints that are not necessarily cone-convex. We show that if a Slater-type cone constraint qualification holds, then every weak minimizer of (VOP) is a KKT point and conversely every KKT point is a weak minimizer. Further a Mond-Weir type dual is formulated in the modified situation and various duality results are established.展开更多
A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products b...A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented.展开更多
In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that se...In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.展开更多
The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional na...The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.展开更多
Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)alg...Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)algorithms.Both optimization algorithms are coupled to one of the three proposed peak finder algorithms.Three custom time-domain algorithms are proposed for retrieving SOP peaks,namely peak seek,slope tangent,and fast array algorithms.In addition,an average combinational algorithm is applied.The time occurrence of the retrieved peaks is tested for an elimination of illusive pulses.Conventional methods are inaccurate and timeconsuming.ALO and PSO optimizations are used for the localization of retrieved peaks.Optimum cost values that achieve the best fitness values are demonstrated.Thus,the optimum positions of the detected peak heights are achieved.Evaluation metrics of the optimized algorithms and their influences on the retrieved peaks parameters are established.Comparisons among such algorithms are investigated,and the algorithms are inspected in terms of their computational time and average error.The peak seek algorithm achieves the lowest average computational error for pulse parameters(amplitude and position).However,the fast array algorithm introduces the largest average error for pulse parameters.In addition,the peak seek algorithm coupled with an ALO or PSO algorithm is observed to realize a better performance in terms of the optimum cost and computational time.By contrast,the performance of the peak seek recovery algorithm is improved using the PSO.Furthermore,the computational time of the peak optimization using the PSO is much better than that of the ALO algorithm.As a final conclusion,the accuracy of the peaks detected by the PSO surpasses that for the peaks detected by the ALO.The implemented peak retrieval algorithms are validated through a comparison with experimental results from previous studies.The proposed algorithms achieve a notable precision for compensation of the SOP peaks within the alpha ray spectroscopy at a high counting rate.展开更多
This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathemat...This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathematics,control,engineering and so on,and thus has received great attention in the past decades.Different from the previous articles where the operator is applied to present the controller,the main contribution of this paper is to propose the discretisation-then-continuousization method,which is explicit and implementable.The solvability condition of the LQ optimal control problems is given based on a set of differential Riccati equations,and an explicit numerical calculation way of these equations and the design of the optimal controller are provided.展开更多
Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the und...Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the underwater environment and have poor robustness against the underwater channel uncertainty, which limit their further application in practical engineering. In this paper, a new method of source localization in shallow water, based on vector optimization concept, is described, which is highly robust against environmental factors affecting the localization, such as the channel depth, the bottom reflection coefficients, and so on. Through constructing the uncertainty set of the source vector errors and extracting the multi-path sound rays from the sea surface and bottom, the proposed method can accurately localize one or more sources in shallow water dominated by multipath propagation. It turns out that the natural formulation of our approach involves minimization of two quadratic functions subject to infinitely many nonconvex quadratic constraints. It shows that this problem （originally intractable） can be reformulated in a convex form as the so-called second-order cone program （SOCP） and solved efficiently by using the well-established interior point method, such as the sottware tool, SeDuMi. Computer simulations show better performance of the proposed method as compared with existing algorithms and establish a theoretical foundation for the practical engineering application.展开更多
A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential correspondi...A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.展开更多
In this paper, we approach the problem of obtaining approximate solution of second-order initial value problems by converting it to an optimization problem. It is assumed that the solution can be approximated by a pol...In this paper, we approach the problem of obtaining approximate solution of second-order initial value problems by converting it to an optimization problem. It is assumed that the solution can be approximated by a polynomial. The coefficients of the polynomial are then optimized using simulated annealing technique. Numerical examples with good results show the accuracy of the proposed approach compared with some existing methods.展开更多
The current sugarcane seeding mechanism is unable to accomplish complex seeding movement trajectories and postures,thus failing to enable the cane seed to enter the seed trench in a stable posture,resulting in a high ...The current sugarcane seeding mechanism is unable to accomplish complex seeding movement trajectories and postures,thus failing to enable the cane seed to enter the seed trench in a stable posture,resulting in a high rate of collapse and a low survival rate.A second-order non-circular planetary gear system pendulum-type seeding mechanism is adopted to realize the complex motion of seeding arm taking seeds in an orderly manner,transporting seeds stably,and sowing seeds in a fixed posture.Constraining the position and posture of the end point of the seeding arm,based on the principle of second-order center distance invariance in the motion process of the planetary gear train,the inverse optimization design model of approximate multi-positional posture is established,and the initial optimal parameters of the double-motion point of the mechanism are solved by genetic algorithm.The second-order non-circular gear ratios are assigned according to the kinematic characteristics of the mechanism in order to design all the non-circular gear pitch curves and model their convexity calculations.In order to avoid the influence on the preset position and posture,the position of the corresponding relative angular displacement fitting point of the adjustable trajectory segment on the closed motion trajectory is taken as the optimization variable,and the convexity optimization model of the second-order non-circular gear pitch curve is established.A set of non-circular gear pitch curves with better roundness is obtained by NSGA II multi-objective optimization algorithm combined with entropy weight TOPSIS game theory.The simulation results show that the motion trajectory posture of the virtual prototype is basically consistent with the theoretical model,which meets the agronomic requirements of sugarcane seeding and verifies the feasibility of the mechanism design.展开更多
This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas sy...This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES.展开更多
A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and qu...A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O（√Nlog N log N/ε） for large-update methods and O（√Nlog N/ε） for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.展开更多
This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable conve...This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable convex functions is chosen as the team objective function.First,based on the local information of each agent’s neighborhood,a novel distributed adaptive optimization algorithm with nonuniform gradient gains is designed,where these gains only have relations with agents’own states.And then,the original closed-loop system is changed into an equivalent one by taking a coordination transformation.Moreover,it is proved that the states including positions and velocities of all agents are bounded by constructing a Lyapunov function provided that the initial values are given.By the theory of Lyapunov stability,it is shown that all agents can finally reach an agreement and their position states converge to the optimal solution of the team objective function asymptotically.Finally,the effectiveness of the obtained theoretical results is demonstrated by several simulation examples.展开更多
This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product o...This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product of second-order cones(here named as Q-multiobjective optimization problem).For an abstract-constrained Q-multiobjective optimization problem,we derive two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions.For Q-multiobjective optimization problem with explicit constraints,we demonstrate first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as second-order sufficient optimality conditions under upper second-order regularity for the explicit constraints.As applications,we obtain optimality conditions for polyhedral conic,second-order conic,and semi-definite conic Q-multiobjective optimization problems.展开更多
In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investig...In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.展开更多
An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Lowner operator associated with a potential function for the optimization problems with inequality ...An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Lowner operator associated with a potential function for the optimization problems with inequality constraints.The favorable properties of both the Lowner operator and the corresponding augmented Lagrangian are discussed.And under some mild assumptions,the rate of convergence of the augmented Lagrange algorithm is studied in detail.展开更多
We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iterat...We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering steps.Here,each iteration consists of only a feasibility step.Thus,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step.The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.展开更多
A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lac...A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lacks interpretability in its results,obscuring the causal relationships between data distribution characteristics and the outcomes.Furthermore,the current approach to battery type selection is not included in traditional BESS planning,hindering comprehensive optimization.To tackle these BESS planning problems,this paper presents a universal method for BESS planning,which is designed to enhance the interpretability of DRO.First,mathematical definitions of interpretable DRO(IDRO)are introduced.Next,the uncertainties in wind power,photovoltaic power,and loads are modeled by using second-order cone ambiguity sets(SOCASs).In addition,the proposed method integrates selection,sizing,and siting.Moreover,a second-order cone bidirectional-orthogonal strategy is proposed to solve the BESS planning problems.Finally,the effectiveness of the proposed method is demonstrated through case studies,offering planners richer decision-making insights.展开更多
基金Special Item of National Major Scientific Apparatus Development(No.2013YQ140431)
文摘When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.
基金The Graduate Students Innovate Scientific Research Program (YJSCX2008-158HLJ) of Heilongjiang Provincesupported by the Distinguished Young Scholar Foundation (JC200707) of Heilongjiang Province of China
文摘In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.
文摘In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently, Lassere [1] considered a scalar programming problem and showed that if the convexity of the constraint functions is replaced by the convexity of the feasible set, this crucial feature of convex programming can still be preserved. In this paper, we generalize his results by making them applicable to vector optimization problems (VOP) over cones. We consider the minimization of a cone-convex function over a convex feasible set described by cone constraints that are not necessarily cone-convex. We show that if a Slater-type cone constraint qualification holds, then every weak minimizer of (VOP) is a KKT point and conversely every KKT point is a weak minimizer. Further a Mond-Weir type dual is formulated in the modified situation and various duality results are established.
文摘A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented.
基金The National Natural Science Foundation of China(No.61231002,61273266,61375028)the Ph.D.Programs Foundation of Ministry of Education of China(No.20110092130004)
文摘In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.
基金supported by the National Natural Science Foundation of China(61803357)。
文摘The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.
文摘Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)algorithms.Both optimization algorithms are coupled to one of the three proposed peak finder algorithms.Three custom time-domain algorithms are proposed for retrieving SOP peaks,namely peak seek,slope tangent,and fast array algorithms.In addition,an average combinational algorithm is applied.The time occurrence of the retrieved peaks is tested for an elimination of illusive pulses.Conventional methods are inaccurate and timeconsuming.ALO and PSO optimizations are used for the localization of retrieved peaks.Optimum cost values that achieve the best fitness values are demonstrated.Thus,the optimum positions of the detected peak heights are achieved.Evaluation metrics of the optimized algorithms and their influences on the retrieved peaks parameters are established.Comparisons among such algorithms are investigated,and the algorithms are inspected in terms of their computational time and average error.The peak seek algorithm achieves the lowest average computational error for pulse parameters(amplitude and position).However,the fast array algorithm introduces the largest average error for pulse parameters.In addition,the peak seek algorithm coupled with an ALO or PSO algorithm is observed to realize a better performance in terms of the optimum cost and computational time.By contrast,the performance of the peak seek recovery algorithm is improved using the PSO.Furthermore,the computational time of the peak optimization using the PSO is much better than that of the ALO algorithm.As a final conclusion,the accuracy of the peaks detected by the PSO surpasses that for the peaks detected by the ALO.The implemented peak retrieval algorithms are validated through a comparison with experimental results from previous studies.The proposed algorithms achieve a notable precision for compensation of the SOP peaks within the alpha ray spectroscopy at a high counting rate.
基金supported by the National Natural Science Foundation of China[grant numbers 61821004,62250056]the Natural Science Foundation of Shandong Province[grant numbers ZR2021ZD14,ZR2021JQ24]+2 种基金Science and Technology Project of Qingdao West Coast New Area[grant numbers 2019-32,2020-20,2020-1-4]High-level Talent Team Project of Qingdao West Coast New Area[grant number RCTD-JC-2019-05]Key Research and Development Program of Shandong Province[grant number 2020CXGC01208].
文摘This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathematics,control,engineering and so on,and thus has received great attention in the past decades.Different from the previous articles where the operator is applied to present the controller,the main contribution of this paper is to propose the discretisation-then-continuousization method,which is explicit and implementable.The solvability condition of the LQ optimal control problems is given based on a set of differential Riccati equations,and an explicit numerical calculation way of these equations and the design of the optimal controller are provided.
基金This Project supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20122304120011)the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No.HEUCFR1119)
文摘Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the underwater environment and have poor robustness against the underwater channel uncertainty, which limit their further application in practical engineering. In this paper, a new method of source localization in shallow water, based on vector optimization concept, is described, which is highly robust against environmental factors affecting the localization, such as the channel depth, the bottom reflection coefficients, and so on. Through constructing the uncertainty set of the source vector errors and extracting the multi-path sound rays from the sea surface and bottom, the proposed method can accurately localize one or more sources in shallow water dominated by multipath propagation. It turns out that the natural formulation of our approach involves minimization of two quadratic functions subject to infinitely many nonconvex quadratic constraints. It shows that this problem （originally intractable） can be reformulated in a convex form as the so-called second-order cone program （SOCP） and solved efficiently by using the well-established interior point method, such as the sottware tool, SeDuMi. Computer simulations show better performance of the proposed method as compared with existing algorithms and establish a theoretical foundation for the practical engineering application.
基金Project supported by the National Natural Science Foundation of China (No. 10771026)the Foundation of Dalian University of Technology (Nos. MXDUT73008 and MXDUT98009)
文摘A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.
文摘In this paper, we approach the problem of obtaining approximate solution of second-order initial value problems by converting it to an optimization problem. It is assumed that the solution can be approximated by a polynomial. The coefficients of the polynomial are then optimized using simulated annealing technique. Numerical examples with good results show the accuracy of the proposed approach compared with some existing methods.
基金supported by The National Natural Science Foundation of China(Grant No.52265028)Guangxi Natural Science Foundation of China(Grant No.2021JJA160046)Innovation Project of Guangxi Graduate Education(Grant No.YCSW2023362).
文摘The current sugarcane seeding mechanism is unable to accomplish complex seeding movement trajectories and postures,thus failing to enable the cane seed to enter the seed trench in a stable posture,resulting in a high rate of collapse and a low survival rate.A second-order non-circular planetary gear system pendulum-type seeding mechanism is adopted to realize the complex motion of seeding arm taking seeds in an orderly manner,transporting seeds stably,and sowing seeds in a fixed posture.Constraining the position and posture of the end point of the seeding arm,based on the principle of second-order center distance invariance in the motion process of the planetary gear train,the inverse optimization design model of approximate multi-positional posture is established,and the initial optimal parameters of the double-motion point of the mechanism are solved by genetic algorithm.The second-order non-circular gear ratios are assigned according to the kinematic characteristics of the mechanism in order to design all the non-circular gear pitch curves and model their convexity calculations.In order to avoid the influence on the preset position and posture,the position of the corresponding relative angular displacement fitting point of the adjustable trajectory segment on the closed motion trajectory is taken as the optimization variable,and the convexity optimization model of the second-order non-circular gear pitch curve is established.A set of non-circular gear pitch curves with better roundness is obtained by NSGA II multi-objective optimization algorithm combined with entropy weight TOPSIS game theory.The simulation results show that the motion trajectory posture of the virtual prototype is basically consistent with the theoretical model,which meets the agronomic requirements of sugarcane seeding and verifies the feasibility of the mechanism design.
基金This work was supported in part by the National Natural Science Foundation of China under Grants 61673161 and 51807134and in part by the program of fundamental research of the Siberian Branch of Russian Academy of Sciences and carried out within the framework of the research project III.17.3.1,Reg.No.AAAA-A17-117030310442-8.
文摘This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES.
文摘A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O（√Nlog N log N/ε） for large-update methods and O（√Nlog N/ε） for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.
基金the National Natural Science Foundation of China under Grant Nos.61973329 and 61772063the Beijing Natural Science Foundation under Grant Nos.Z180005 and 9192008。
文摘This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable convex functions is chosen as the team objective function.First,based on the local information of each agent’s neighborhood,a novel distributed adaptive optimization algorithm with nonuniform gradient gains is designed,where these gains only have relations with agents’own states.And then,the original closed-loop system is changed into an equivalent one by taking a coordination transformation.Moreover,it is proved that the states including positions and velocities of all agents are bounded by constructing a Lyapunov function provided that the initial values are given.By the theory of Lyapunov stability,it is shown that all agents can finally reach an agreement and their position states converge to the optimal solution of the team objective function asymptotically.Finally,the effectiveness of the obtained theoretical results is demonstrated by several simulation examples.
基金This work was supported by the National Natural Science Foundation of China(Nos.11571059,11731013 and 91330206).
文摘This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product of second-order cones(here named as Q-multiobjective optimization problem).For an abstract-constrained Q-multiobjective optimization problem,we derive two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions.For Q-multiobjective optimization problem with explicit constraints,we demonstrate first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as second-order sufficient optimality conditions under upper second-order regularity for the explicit constraints.As applications,we obtain optimality conditions for polyhedral conic,second-order conic,and semi-definite conic Q-multiobjective optimization problems.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11601437,11526165and 11571055the Scientific Research Fund of Sichuan Provincial Science and Technology Department under Grant No.2015JY0237the Fundamental Research Funds for the Central Universities under Grant No.JBK160129
文摘In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.
基金supported by the Fundamental Research Funds for the Central Universities(No.2018IB016).
文摘An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Lowner operator associated with a potential function for the optimization problems with inequality constraints.The favorable properties of both the Lowner operator and the corresponding augmented Lagrangian are discussed.And under some mild assumptions,the rate of convergence of the augmented Lagrange algorithm is studied in detail.
文摘We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering steps.Here,each iteration consists of only a feasibility step.Thus,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step.The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.
基金supported by the National Natural Science Foundation of China(No.51977046)。
文摘A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lacks interpretability in its results,obscuring the causal relationships between data distribution characteristics and the outcomes.Furthermore,the current approach to battery type selection is not included in traditional BESS planning,hindering comprehensive optimization.To tackle these BESS planning problems,this paper presents a universal method for BESS planning,which is designed to enhance the interpretability of DRO.First,mathematical definitions of interpretable DRO(IDRO)are introduced.Next,the uncertainties in wind power,photovoltaic power,and loads are modeled by using second-order cone ambiguity sets(SOCASs).In addition,the proposed method integrates selection,sizing,and siting.Moreover,a second-order cone bidirectional-orthogonal strategy is proposed to solve the BESS planning problems.Finally,the effectiveness of the proposed method is demonstrated through case studies,offering planners richer decision-making insights.
