In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter...In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the sufficient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is effective.展开更多
In this paper,we present a QP-free algorithm without a penalty function or a filter for nonlinear semidefinite programming.At each iteration,two systems of linear equations with the same coefficient matrix are solved ...In this paper,we present a QP-free algorithm without a penalty function or a filter for nonlinear semidefinite programming.At each iteration,two systems of linear equations with the same coefficient matrix are solved to determine search direction;the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced.There is no feasibility restoration phase in our algorithm,which is necessary for traditional filter methods.The proposed algorithm is globally convergent under some mild conditions.Preliminary numerical results indicate that the proposed algorithm is comparable.展开更多
We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming.At each iteration,we solve a linear semidefinite programming to test whether the linearized constraints are ...We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming.At each iteration,we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not.The search direction is generated by a piecewise quadratic-linear model of the exact penalty function.The penalty parameter is only related to the information of the current iterate point.The line search strategy is a penalty-free one.Global and local convergence are analyzed under suitable conditions.We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.展开更多
In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,...In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,is established under certain conditions of convexity.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11061011 and 11361018)Guangxi Fund for Distinguished Young Scholars(Grant No.2012GXNSFFA060003)+2 种基金the Guangxi Fund(Grant No.2013GXNSFDA019002)the first author would like to thank the Project of Guangxi Innovation Team"Optimization method and its engineering application"(Grant No.2014GXNSFFA118001)supported by Guangxi Experiment Center of Information Science and Guangxi Key Laboratory of Automatic Detecting Technology and Instruments
文摘In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the sufficient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is effective.
基金supported by the National Natural Science Foundation(No.11561005)the National Science Foundation of Guangxi(No.2016GXNSFAA380248)。
文摘In this paper,we present a QP-free algorithm without a penalty function or a filter for nonlinear semidefinite programming.At each iteration,two systems of linear equations with the same coefficient matrix are solved to determine search direction;the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced.There is no feasibility restoration phase in our algorithm,which is necessary for traditional filter methods.The proposed algorithm is globally convergent under some mild conditions.Preliminary numerical results indicate that the proposed algorithm is comparable.
基金supported by the National Natural Science Foundation of China(Nos.11871362)。
文摘We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming.At each iteration,we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not.The search direction is generated by a piecewise quadratic-linear model of the exact penalty function.The penalty parameter is only related to the information of the current iterate point.The line search strategy is a penalty-free one.Global and local convergence are analyzed under suitable conditions.We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.
基金supported by the National Natural Science Foundation of China under Grant No. 10871098the Natural Science Fund of Jiangsu Province under Grant No. BK2009397the Innovation Fund of Youth of Fujian Province under Grant No. 2009J05003 and CNPq Brazil
文摘In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,is established under certain conditions of convexity.
