In this paper,a linear optimization method(LOM)for the design of terahertz circuits is presented,aimed at enhancing the simulation efficacy and reducing the time of the circuit design workflow.This method enables the ...In this paper,a linear optimization method(LOM)for the design of terahertz circuits is presented,aimed at enhancing the simulation efficacy and reducing the time of the circuit design workflow.This method enables the rapid determination of optimal embedding impedance for diodes across a specific bandwidth to achieve maximum efficiency through harmonic balance simulations.By optimizing the linear matching circuit with the optimal embedding impedance,the method effectively segregates the simulation of the linear segments from the nonlinear segments in the frequency multiplier circuit,substantially improving the speed of simulations.The design of on-chip linear matching circuits adopts a modular circuit design strategy,incorporating fixed load resistors to simplify the matching challenge.Utilizing this approach,a 340 GHz frequency doubler was developed and measured.The results demonstrate that,across a bandwidth of 330 GHz to 342 GHz,the efficiency of the doubler remains above 10%,with an input power ranging from 98 mW to 141mW and an output power exceeding 13 mW.Notably,at an input power of 141 mW,a peak output power of 21.8 mW was achieved at 334 GHz,corresponding to an efficiency of 15.8%.展开更多
In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barr...In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.展开更多
The objective of this study is to develop a wind farm placement and investment methodology based on a linear optimization procedure.This problem has a major significance for the investment success for the projects of ...The objective of this study is to develop a wind farm placement and investment methodology based on a linear optimization procedure.This problem has a major significance for the investment success for the projects of renewable energy such as wind power.In this study,a mesoscale approach is adopted whereby the wind farm location is investigated in comparison with a microscale approach where the location of each individual turbine is optimized.Specifical study focuses on the placement of a wind farm by economical optimization constrained by the power system,wind resources,and techno-economics.Linear optimization is introduced in this context at the power system which is constrained by wind farm planning.展开更多
The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（ga...The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.展开更多
Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research metho...Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.展开更多
A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided proje...A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.展开更多
In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatu...In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.展开更多
This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function...This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.展开更多
In this paper, the map of a network of air routes was updated by removing the non-optimal routes and replacing them with the best ones. An integer linear programming model was developed. The aim was to find optimal ro...In this paper, the map of a network of air routes was updated by removing the non-optimal routes and replacing them with the best ones. An integer linear programming model was developed. The aim was to find optimal routes in superspace based on performance-based navigation. The optimal routes were found from a DIJKSTRA algorithm that calculates the shortest path in a graph. Simulations with python language on real traffic areas showed the improvements brought by surface navigation. In this work, the conceptual phase and the upper airspace were studied.展开更多
The Robogymnast is a triple link underactuated pendulum that mimics a human gymnast hanging from a horizontal bar.In this paper, two multi-objective optimization methods are developed using invasive weed optimization...The Robogymnast is a triple link underactuated pendulum that mimics a human gymnast hanging from a horizontal bar.In this paper, two multi-objective optimization methods are developed using invasive weed optimization（IWO）. The first method is the weighted criteria method IWO（WCMIWO） and the second method is the fuzzy logic IWO hybrid（FLIWOH）. The two optimization methods were used to investigate the optimum diagonal values for the Q matrix of the linear quadratic regulator（LQR） controller that can balance the Robogymnast in an upright configuration. Two LQR controllers were first developed using the parameters obtained from the two optimization methods. The same process was then repeated, but this time with disturbance applied to the Robogymnast states to develop another set of two LQR controllers. The response of the controllers was then tested in different scenarios using simulation and their performance evaluated. The results show that all four controllers are able to balance the Robogymnast with varying accuracies. It has also been observed that the controllers trained with disturbance achieve faster settling time.展开更多
In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery p...In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.展开更多
In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of...In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.展开更多
In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this...In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this framework,in contrast to the classical LQ issue,embodies that the admissible control set needs to satisfy more than the square integrability.By introducing two kinds of new generalized Riccati equations,we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation.A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited.Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized,and associated efficient portfolios are given in a closed form.展开更多
This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)...This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)framework.For the MFS control problem,this review discusses the existing conclusions on optimization in dynamic systems affected by both additive and multiplicative noises.In exploring MFT optimization,the authors first revisit researches associated with single-player systems constrained by these dynamics.The authors then extend the proposed review to scenarios that include multiple players engaged in Nash games,Stackelberg games,and cooperative Pareto games.Finally,the paper concludes by emphasizing future research on intelligent algorithms for mean field optimization,particularly using reinforcement learning method to design strategies for models with unknown parameters.展开更多
In oil and mineral exploration, gravity gradient tensor data include higher- frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry （FTG） data are...In oil and mineral exploration, gravity gradient tensor data include higher- frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry （FTG） data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient tensor data. We first derive the Cartesian equations of gravity gradient tensors under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient tensor data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high- frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient tensor data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.展开更多
The choice of self-concordant functions is the key to efficient algorithms for linear and quadratic convex optimizations, which provide a method with polynomial-time iterations to solve linear and quadratic convex opt...The choice of self-concordant functions is the key to efficient algorithms for linear and quadratic convex optimizations, which provide a method with polynomial-time iterations to solve linear and quadratic convex optimization problems. The parameters of a self-concordant barrier function can be used to compute the complexity bound of the proposed algorithm. In this paper, it is proved that the finite barrier function is a local self-concordant barrier function. By deriving the local values of parameters of this barrier function, the desired complexity bound of an interior-point algorithm based on this local self-concordant function for linear optimization problem is obtained. The bound matches the best known bound for small-update methods.展开更多
In this paper, the relationship between steel and chemical elements is explored. A production record of a steel mill is adopted for two years, which is used as the basic data to standardize the data. Then, according t...In this paper, the relationship between steel and chemical elements is explored. A production record of a steel mill is adopted for two years, which is used as the basic data to standardize the data. Then, according to the correlation coefficient method between the hot-rolled ribs No. 1 and No. 2 hot-rolled ribs, the correlation between the two sets of data is analyzed. The main influencing factors of the hot-rolled ribs properties are obtained qualitatively. Then, the logistic regression method is used. Finally, according to the national standard of Chinese steel, the linear optimization model of Cr and Mn and V elements was established, and the change range of Cr was obtained without affecting the performance of hot rolled ribs.展开更多
Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method...Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneousiy provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking （LQT） control method.展开更多
Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model ...Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model was established for a single-source multi-distribution oil pro- duct pipeline, and scheduling plans were made based on supply. In the model, time node constraints, oil offloading plan constraints, and migration of batch constraints were taken into consideration. The minimum deviation between the demanded oil volumes and the actual offloading volumes was chosen as the objective function, and a linear programming model was established on the basis of known time nodes＇ sequence. The ant colony optimization algo- rithm and simplex method were used to solve the model. The model was applied to a real pipeline and it performed well.展开更多
This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a ...This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a current dipole and volume currents. Then by using the simulated magnetic fields based on torso-heart model as input, the cardiac current sources--an array of current dipoles by optimal constrained linear inverse method are constructed. Next, the current dipole array reconstruction considering boundaries is compared with that in an unbounded homogeneous medium. Furthermore, the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.展开更多
基金Supported by the Beijing Municipal Science&Technology Commission(Z211100004421012),the Key Reaserch and Development Pro⁃gram of China(2022YFF0605902)。
文摘In this paper,a linear optimization method(LOM)for the design of terahertz circuits is presented,aimed at enhancing the simulation efficacy and reducing the time of the circuit design workflow.This method enables the rapid determination of optimal embedding impedance for diodes across a specific bandwidth to achieve maximum efficiency through harmonic balance simulations.By optimizing the linear matching circuit with the optimal embedding impedance,the method effectively segregates the simulation of the linear segments from the nonlinear segments in the frequency multiplier circuit,substantially improving the speed of simulations.The design of on-chip linear matching circuits adopts a modular circuit design strategy,incorporating fixed load resistors to simplify the matching challenge.Utilizing this approach,a 340 GHz frequency doubler was developed and measured.The results demonstrate that,across a bandwidth of 330 GHz to 342 GHz,the efficiency of the doubler remains above 10%,with an input power ranging from 98 mW to 141mW and an output power exceeding 13 mW.Notably,at an input power of 141 mW,a peak output power of 21.8 mW was achieved at 334 GHz,corresponding to an efficiency of 15.8%.
基金Supported by the Natural Science Foundation of Hubei Province (2008CDZD47)
文摘In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.
基金supported by TUBITAK Scholarship(No.B.14.2.TBT.0.06.01-214-6041)Yildiz Technical University Scientific Project Coordination Fund(No.2012-04-02-DOP04)。
文摘The objective of this study is to develop a wind farm placement and investment methodology based on a linear optimization procedure.This problem has a major significance for the investment success for the projects of renewable energy such as wind power.In this study,a mesoscale approach is adopted whereby the wind farm location is investigated in comparison with a microscale approach where the location of each individual turbine is optimized.Specifical study focuses on the placement of a wind farm by economical optimization constrained by the power system,wind resources,and techno-economics.Linear optimization is introduced in this context at the power system which is constrained by wind farm planning.
基金supported by the National Natural Science Foundation of China(6132106261503100)the China Postdoctoral Science Foundation(2014M550189)
文摘The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.
文摘Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.
文摘A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.
文摘In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.
文摘This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.
文摘In this paper, the map of a network of air routes was updated by removing the non-optimal routes and replacing them with the best ones. An integer linear programming model was developed. The aim was to find optimal routes in superspace based on performance-based navigation. The optimal routes were found from a DIJKSTRA algorithm that calculates the shortest path in a graph. Simulations with python language on real traffic areas showed the improvements brought by surface navigation. In this work, the conceptual phase and the upper airspace were studied.
基金Majlis Amanah Rakyat (MARA)German Malaysian Institute (GMI) for their sponsorship
文摘The Robogymnast is a triple link underactuated pendulum that mimics a human gymnast hanging from a horizontal bar.In this paper, two multi-objective optimization methods are developed using invasive weed optimization（IWO）. The first method is the weighted criteria method IWO（WCMIWO） and the second method is the fuzzy logic IWO hybrid（FLIWOH）. The two optimization methods were used to investigate the optimum diagonal values for the Q matrix of the linear quadratic regulator（LQR） controller that can balance the Robogymnast in an upright configuration. Two LQR controllers were first developed using the parameters obtained from the two optimization methods. The same process was then repeated, but this time with disturbance applied to the Robogymnast states to develop another set of two LQR controllers. The response of the controllers was then tested in different scenarios using simulation and their performance evaluated. The results show that all four controllers are able to balance the Robogymnast with varying accuracies. It has also been observed that the controllers trained with disturbance achieve faster settling time.
基金Supported by the National Fund of Natural Sciences.
文摘In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.
文摘In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.
基金financial support partly by the National Nature Science Foundation of China(Grant No.12171053,11701040,11871010&61871058)the Fundamental Research Funds for the Central Universities+2 种基金the Research Funds of Renmin University of China(No.23XNKJ05)the financial support partly by the National Nature Science Foundation of China(Grant No.11871010,11971040)the Fundamental Research Funds for the Central Universities(No.2019XD-A11).
文摘In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this framework,in contrast to the classical LQ issue,embodies that the admissible control set needs to satisfy more than the square integrability.By introducing two kinds of new generalized Riccati equations,we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation.A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited.Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized,and associated efficient portfolios are given in a closed form.
基金supported by the National Natural Science Foundation of China under Grant Nos.62103442,12326343,62373229the Research Grants Council of the Hong Kong Special Administrative Region,China under Grant Nos.CityU 11213023,11205724+3 种基金the Natural Science Foundation of Shandong Province under Grant No.ZR2021QF080the Taishan Scholar Project of Shandong Province under Grant No.tsqn202408110the Fundamental Research Foundation of the Central Universities under Grant No.23CX06024Athe Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant No.2023KJ061.
文摘This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)framework.For the MFS control problem,this review discusses the existing conclusions on optimization in dynamic systems affected by both additive and multiplicative noises.In exploring MFT optimization,the authors first revisit researches associated with single-player systems constrained by these dynamics.The authors then extend the proposed review to scenarios that include multiple players engaged in Nash games,Stackelberg games,and cooperative Pareto games.Finally,the paper concludes by emphasizing future research on intelligent algorithms for mean field optimization,particularly using reinforcement learning method to design strategies for models with unknown parameters.
基金financially supported by the SinoProbe-09-01(201011078)
文摘In oil and mineral exploration, gravity gradient tensor data include higher- frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry （FTG） data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient tensor data. We first derive the Cartesian equations of gravity gradient tensors under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient tensor data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high- frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient tensor data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.
基金supported by the National Natural Science Foundation of China (Grant No.10771133)the Shanghai Leading Academic Discipline Project (Grant No.S30101)the Research Foundation for the Doctoral Program of Higher Education (Grant No.200802800010)
文摘The choice of self-concordant functions is the key to efficient algorithms for linear and quadratic convex optimizations, which provide a method with polynomial-time iterations to solve linear and quadratic convex optimization problems. The parameters of a self-concordant barrier function can be used to compute the complexity bound of the proposed algorithm. In this paper, it is proved that the finite barrier function is a local self-concordant barrier function. By deriving the local values of parameters of this barrier function, the desired complexity bound of an interior-point algorithm based on this local self-concordant function for linear optimization problem is obtained. The bound matches the best known bound for small-update methods.
文摘In this paper, the relationship between steel and chemical elements is explored. A production record of a steel mill is adopted for two years, which is used as the basic data to standardize the data. Then, according to the correlation coefficient method between the hot-rolled ribs No. 1 and No. 2 hot-rolled ribs, the correlation between the two sets of data is analyzed. The main influencing factors of the hot-rolled ribs properties are obtained qualitatively. Then, the logistic regression method is used. Finally, according to the national standard of Chinese steel, the linear optimization model of Cr and Mn and V elements was established, and the change range of Cr was obtained without affecting the performance of hot rolled ribs.
基金supported by the National Natural Science Foundation of China(61573090)the Research Funds for the Central Universities(N130108001)
文摘Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneousiy provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking （LQT） control method.
基金part of the Program of"Study on the mechanism of complex heat and mass transfer during batch transport process in products pipelines"funded under the National Natural Science Foundation of China(grant number 51474228)
文摘Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model was established for a single-source multi-distribution oil pro- duct pipeline, and scheduling plans were made based on supply. In the model, time node constraints, oil offloading plan constraints, and migration of batch constraints were taken into consideration. The minimum deviation between the demanded oil volumes and the actual offloading volumes was chosen as the objective function, and a linear programming model was established on the basis of known time nodes＇ sequence. The ant colony optimization algo- rithm and simplex method were used to solve the model. The model was applied to a real pipeline and it performed well.
基金Project supported by the State Key Development Program for Basic Research of China(Grant No.2006CB601007)the National Natural Science Foundation of China(Grant No.10674006)the National High Technology Research and Development Program of China(Grant No.2007AA03Z238)
文摘This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a current dipole and volume currents. Then by using the simulated magnetic fields based on torso-heart model as input, the cardiac current sources--an array of current dipoles by optimal constrained linear inverse method are constructed. Next, the current dipole array reconstruction considering boundaries is compared with that in an unbounded homogeneous medium. Furthermore, the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.
