A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the...A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.展开更多
The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is signifi...The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.展开更多
How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficien...How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network(DR‐NTZNN)form‐finding algorithm is established through analysing the physical properties of tensegrity structures.In addition,the non‐linear constrained opti-misation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm.Moreover,the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course,disturbance caused by external force and manufacturing error when constructing a tensegrity structure.Hence,for the purpose of suppressing the noise,a noise tolerant zeroing neural network is presented to solve the search direction,which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability.Besides,the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired.The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology.Eventually,comparing with other existing form‐finding methods,the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm.展开更多
It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general...It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general semide finite programming even if both the primal problem and its dual problem are strictly feasible. Some other properties are also concerned.展开更多
This paper is concerned with a class of convex multivariable nonlinear program problems. By virtue of linearization philosophy, a linearization problem (LP) is constructed and theoretical equivalence between (LP) and ...This paper is concerned with a class of convex multivariable nonlinear program problems. By virtue of linearization philosophy, a linearization problem (LP) is constructed and theoretical equivalence between (LP) and the original problem established. Based on relaxation techniques an algorithm for solving (LP) is proposed, which is efficient from a computational viewpoint, since at each iteration the only program that needs to solve is a standard linear program. Furthermore, the optimality criterion is derived. The convergence analysis conducted in this paper indicates that the algorithm guarantees finite ε convergence.展开更多
Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWL...Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.展开更多
基金Fundamental Research Funds for the Central Universities,China(No.2232019D3-38)Shanghai Sailing Program,China(No.22YF1400900)。
文摘A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.
基金supported by the National Science Foundation of China (70771080)Social Science Foundation of Ministry of Education (10YJC630233)
文摘The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
基金supported in part by the National Natural Science Foundation of China under grants 61873304,62173048,62106023in part by the China Postdoctoral Science Foundation Funded Project under grants 2018M641784 and 2019T120240+1 种基金also in part by the Key Science and Technology Projects of Jilin Province,China,under grant 20210201106GXalso in part by the Changchun Science and Technology Project under grant 21ZY41.
文摘How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network(DR‐NTZNN)form‐finding algorithm is established through analysing the physical properties of tensegrity structures.In addition,the non‐linear constrained opti-misation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm.Moreover,the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course,disturbance caused by external force and manufacturing error when constructing a tensegrity structure.Hence,for the purpose of suppressing the noise,a noise tolerant zeroing neural network is presented to solve the search direction,which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability.Besides,the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired.The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology.Eventually,comparing with other existing form‐finding methods,the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm.
文摘It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general semide finite programming even if both the primal problem and its dual problem are strictly feasible. Some other properties are also concerned.
文摘This paper is concerned with a class of convex multivariable nonlinear program problems. By virtue of linearization philosophy, a linearization problem (LP) is constructed and theoretical equivalence between (LP) and the original problem established. Based on relaxation techniques an algorithm for solving (LP) is proposed, which is efficient from a computational viewpoint, since at each iteration the only program that needs to solve is a standard linear program. Furthermore, the optimality criterion is derived. The convergence analysis conducted in this paper indicates that the algorithm guarantees finite ε convergence.
基金supported by the National Natural Science Foundation of China(61201282)the Science and Technology on Communication Information Security Control Laboratory Foundation(9140C130304120C13064)
文摘Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.
