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 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
Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algor...Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.展开更多
To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple...To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output(MIMO) systems.The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors.The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation(BSS) subject to the second-order cone constraint,which can be called as second-order cone programing optimization problem.Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals.Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages.Simulation results verify that the capacity gain and bit error rate(BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem.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
A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorith...A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.展开更多
In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w...In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.展开更多
The variable and unpredictable nature of renewable energy generation(REG)presents challenges to its large-scale integration and the efficient and economic operation of the electricity network,particularly at the distr...The variable and unpredictable nature of renewable energy generation(REG)presents challenges to its large-scale integration and the efficient and economic operation of the electricity network,particularly at the distribution level.In this paper,an operational coordination optimization method is proposed for the electricity and natural gas networks,aiming to overcome the identified negative impacts.The method involves the implementation of bi-directional energy flows through power-to-gas units and gas-fired power plants.A detailed model of the three-phase power distribution system up to each phase is employed to improve the representation of multi-energy systems to consider real-world end-user consumption.This method allows for the full consideration of unbalanced operational scenarios.Meanwhile,the natural gas network is modelled and analyzed with steady-state gas flows and the dynamics of the line pack in pipelines.The sequential symmetrical second-order cone programming(SS-SOCP)method is employed to facilitate the simultaneous analysis of three-phase imbalance and line pack while accelerating the solution process.The efficacy of the operational coordination optimization method is demonstrated in case studies comprising a modified IEEE 123-node power distribution system with a 20-node natural gas network.The studies show that the operational coordination optimization method can simultaneously minimize the total operational cost,the curtailment of installed REG,the voltage imbalance of three-phase power system,and the overall carbon emissions.展开更多
An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a...An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a nonlinear optimal control problem,which is difficult to solve due to the existence of nonlinear kinematics and nonconvex constraints.After convexification treatments and discretization,the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming(SOCP)problems,which can be readily solved by state-of-the-art Interior-Point Methods(IPMs).To mitigate the sensibility of the algorithm on the user-provided initial profile,a Two-Stage Sequential Convex Programming(TSSCP)method is presented in detail.Furthermore,numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance problem.The research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation.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
Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also...Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also presented to optimize these criteria chosen. There are many drawbacks in these methods. In this paper, we introduce a unified framework for optimal design of temporal and spatial filters. Most of the optimal design problems of FIR filters and beamformers are included in the framework. It is shown that all the design problems can be reformulated as convex optimization form as the second-order cone programming （SOCP） and solved efficiently via the well-established interior point methods. The main advantage of our SOCP approach as compared with earlier approaches is that it can include most of the existing methods as its special cases, which leads to more flexible designs. Furthermore, the SOCP approach can optimize multiple required performance measures, which is the drawback of earlier approaches. The SOCP approach is also developed to optimally design temporal and spatial two-dimensional filter and spatial matrix filter. Numerical results demonstrate the effectiveness of the proposed approach.展开更多
Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a noncon...Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints.In this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints.展开更多
Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of...Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker point.Moreover,this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker point.Interestingly,the analysis does not need the strict complementarity condition.展开更多
In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.S...In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.Specifically,the algorithm that we investigate incorporates a specially designed nonsmooth(generalized)Newton step to furnish a second-order update rule for the multipliers.We first show in a unified fashion that under a few abstract assumptions,the proposed method is locally convergent and possesses a(nonasymptotic)superlinear convergence rate,even though the penalty parameter is fixed and/or the strict complementarity fails.Subsequently,we demonstrate that for the three typical scenarios,i.e.,the classic nonlinear programming,the nonlinear second-order cone programming and the nonlinear semidefinite programming,these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that are assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict complementarity.展开更多
In high-speed multiuser Time Reversal(TR)downlink systems,the transmission rate is degraded due to the presence of severe inter-user and inter-symbol interference.Moreover,maximizing the weighted sum rate in such syst...In high-speed multiuser Time Reversal(TR)downlink systems,the transmission rate is degraded due to the presence of severe inter-user and inter-symbol interference.Moreover,maximizing the weighted sum rate in such systems is a critical objective,since the weighting factors represent the priority of different users in different applications.However,it faces significant challenges as it is an NP-hard and non-convex problem.In order to suppress these interferences and maximize the weighted sum rate,in this paper we present a novel approach for the joint design of the pre-filters.The proposed method applies successive convex approximation to transform the original problem into a Second-Order Cone Programming(SOCP)problem.Then,a low-complexity iterative algorithm is provided to effectively solve the resulting SOCP problem.According to the simulation results,the proposed method reaches a local optimum within a few iterations and demonstrates superior performance in terms of weighted sum rate compared to the current algorithm.展开更多
This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be ...This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be found in polynomial time.When the feasible region is unbounded,a semidefinite programming(SDP)reformulation is constructed to find the optimal objective value of the original problem in polynomial time.In addition,we provide two sufficient conditions,under which,if the optimal objective value is finite,we show the optimal solution of SDP reformulation can be decomposed into the original space to generate an optimal solution of the original problem in polynomial time.Otherwise,a recession direction can be identified in polynomial time.Numerical examples are included to illustrate the effectiveness of the proposed approach.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 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 (Nos. 71061002 and 11071158)the Natural Science Foundation of Guangxi Province of China (Nos. 0832052 and 2010GXNSFB013047)
文摘Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.
基金supported by Sichuan Youth Science and Technology Innovation Research Team Project(No.2015TD0022)the Talents Project of Sichuan University of Science and Engineering(No.2017RCL11 and No.2017RCL10)the first batch of science and technology plan key R&D project of Sichuan province(No.2017GZ0068)
文摘To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output(MIMO) systems.The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors.The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation(BSS) subject to the second-order cone constraint,which can be called as second-order cone programing optimization problem.Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals.Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages.Simulation results verify that the capacity gain and bit error rate(BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem.
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.
基金the National Science Foundation(60574075, 60674108)
文摘A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.
基金supported by the National Natural Science Foundation of China(11401126,71471140 and 11361018)Guangxi Natural Science Foundation(2016GXNSFBA380102 and 2014GXNSFFA118001)+2 种基金Guangxi Key Laboratory of Cryptography and Information Security(GCIS201618)Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112 and YQ16112)China
文摘In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.
基金supported by the Engineering and Physical Sciences Research Council(EPSRC,UK)in project“Street2Grid–an electricity blockchain platform for P2P energy trading”(No.EP/S001778/2).
文摘The variable and unpredictable nature of renewable energy generation(REG)presents challenges to its large-scale integration and the efficient and economic operation of the electricity network,particularly at the distribution level.In this paper,an operational coordination optimization method is proposed for the electricity and natural gas networks,aiming to overcome the identified negative impacts.The method involves the implementation of bi-directional energy flows through power-to-gas units and gas-fired power plants.A detailed model of the three-phase power distribution system up to each phase is employed to improve the representation of multi-energy systems to consider real-world end-user consumption.This method allows for the full consideration of unbalanced operational scenarios.Meanwhile,the natural gas network is modelled and analyzed with steady-state gas flows and the dynamics of the line pack in pipelines.The sequential symmetrical second-order cone programming(SS-SOCP)method is employed to facilitate the simultaneous analysis of three-phase imbalance and line pack while accelerating the solution process.The efficacy of the operational coordination optimization method is demonstrated in case studies comprising a modified IEEE 123-node power distribution system with a 20-node natural gas network.The studies show that the operational coordination optimization method can simultaneously minimize the total operational cost,the curtailment of installed REG,the voltage imbalance of three-phase power system,and the overall carbon emissions.
基金supported by the Joint Foundation of the Ministry of Education of China(No.6141A02022340).
文摘An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a nonlinear optimal control problem,which is difficult to solve due to the existence of nonlinear kinematics and nonconvex constraints.After convexification treatments and discretization,the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming(SOCP)problems,which can be readily solved by state-of-the-art Interior-Point Methods(IPMs).To mitigate the sensibility of the algorithm on the user-provided initial profile,a Two-Stage Sequential Convex Programming(TSSCP)method is presented in detail.Furthermore,numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance problem.The research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation.
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.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 60472073） the Doctorate Foundation of Northwestern Polytechnical University.
文摘Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also presented to optimize these criteria chosen. There are many drawbacks in these methods. In this paper, we introduce a unified framework for optimal design of temporal and spatial filters. Most of the optimal design problems of FIR filters and beamformers are included in the framework. It is shown that all the design problems can be reformulated as convex optimization form as the second-order cone programming （SOCP） and solved efficiently via the well-established interior point methods. The main advantage of our SOCP approach as compared with earlier approaches is that it can include most of the existing methods as its special cases, which leads to more flexible designs. Furthermore, the SOCP approach can optimize multiple required performance measures, which is the drawback of earlier approaches. The SOCP approach is also developed to optimally design temporal and spatial two-dimensional filter and spatial matrix filter. Numerical results demonstrate the effectiveness of the proposed approach.
基金supported by US Army Research Office Grant(No.W911NF-04-D-0003)by the North Carolina State University Edward P.Fitts Fellowship and by National Natural Science Foundation of China(No.11171177)。
文摘Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints.In this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints.
基金supported by National Natural Science Foundation of China(Grant Nos.10771026,10901094)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of China
文摘Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker point.Moreover,this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker point.Interestingly,the analysis does not need the strict complementarity condition.
基金supported by National Natural Science Foundation of China (Grant No. 11801158)the Hunan Provincial Natural Science Foundation of China (Grant No. 2019JJ50040)+2 种基金the Fundamental Research Funds for the Central Universities in Chinasupported by National Natural Science Foundation of China (Grant No. 11871002)the General Program of Science and Technology of Beijing Municipal Education Commission (Grant No. KM201810005004)
文摘In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.Specifically,the algorithm that we investigate incorporates a specially designed nonsmooth(generalized)Newton step to furnish a second-order update rule for the multipliers.We first show in a unified fashion that under a few abstract assumptions,the proposed method is locally convergent and possesses a(nonasymptotic)superlinear convergence rate,even though the penalty parameter is fixed and/or the strict complementarity fails.Subsequently,we demonstrate that for the three typical scenarios,i.e.,the classic nonlinear programming,the nonlinear second-order cone programming and the nonlinear semidefinite programming,these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that are assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict complementarity.
基金partially supported by the following funding sources:The National Natural Science Foundation of China(No.61771084)the Chongqing Graduate Scientific Research Innovation Project(No.CYB21200)。
文摘In high-speed multiuser Time Reversal(TR)downlink systems,the transmission rate is degraded due to the presence of severe inter-user and inter-symbol interference.Moreover,maximizing the weighted sum rate in such systems is a critical objective,since the weighting factors represent the priority of different users in different applications.However,it faces significant challenges as it is an NP-hard and non-convex problem.In order to suppress these interferences and maximize the weighted sum rate,in this paper we present a novel approach for the joint design of the pre-filters.The proposed method applies successive convex approximation to transform the original problem into a Second-Order Cone Programming(SOCP)problem.Then,a low-complexity iterative algorithm is provided to effectively solve the resulting SOCP problem.According to the simulation results,the proposed method reaches a local optimum within a few iterations and demonstrates superior performance in terms of weighted sum rate compared to the current algorithm.
基金Fang was supported by the US National Science Foundation(No.DMI-0553310)Guo,Wang and Xing were supported by the National Natural Science Foundation of China(Nos.11171177 and 11371216)Deng was supported by the Edward P.Fitts Fellowship at North Carolina State University.
文摘This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be found in polynomial time.When the feasible region is unbounded,a semidefinite programming(SDP)reformulation is constructed to find the optimal objective value of the original problem in polynomial time.In addition,we provide two sufficient conditions,under which,if the optimal objective value is finite,we show the optimal solution of SDP reformulation can be decomposed into the original space to generate an optimal solution of the original problem in polynomial time.Otherwise,a recession direction can be identified in polynomial time.Numerical examples are included to illustrate the effectiveness of the proposed approach.
基金supported by the Natural Science Foundation of Hubei Province(2011CDC028)the Key Project of Hubei Provincial Department of Education(D20122701)+1 种基金the Excellent Youth Project of Hubei Provincial Department of Education(Q20122709)the Doctorial Foundation of Huanggang Normal University(2011CD292,08CD158)
