In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale...In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.展开更多
This paper presents a trust region algorithm for nonlinear optimization with linear inequality constraints. The global convergence of the algorithm is proved. Local quadratic convergence is obtained for a strong local...This paper presents a trust region algorithm for nonlinear optimization with linear inequality constraints. The global convergence of the algorithm is proved. Local quadratic convergence is obtained for a strong local minimizer.展开更多
A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization pro...A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.展开更多
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, a new trust region algorithm for minimax optimization problems is proposed, which solves only one quadratic subproblem based on a new approximation model at each iteration. The approach is different wit...In this paper, a new trust region algorithm for minimax optimization problems is proposed, which solves only one quadratic subproblem based on a new approximation model at each iteration. The approach is different with the traditional algorithms that usually require to solve two quadratic subproblems. Moreover, to avoid Maratos effect, the nonmonotone strategy is employed. The analysis shows that, under standard conditions, the algorithm has global and superlinear convergence. Preliminary numerical experiments are conducted to show the effiency of the new method.展开更多
An efficient SQP algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack va...An efficient SQP algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the 1∞ exact penalty function through Armijo-type line search scheme. The algorithm is proved to be convergent globally under mild conditions.展开更多
基金The subject is supported by Natural Science Foundation of China and Natural Science Foundation of Shandong Province.
文摘In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.
文摘This paper presents a trust region algorithm for nonlinear optimization with linear inequality constraints. The global convergence of the algorithm is proved. Local quadratic convergence is obtained for a strong local minimizer.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10571137,10771162)
文摘A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.
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.
文摘In this paper, a new trust region algorithm for minimax optimization problems is proposed, which solves only one quadratic subproblem based on a new approximation model at each iteration. The approach is different with the traditional algorithms that usually require to solve two quadratic subproblems. Moreover, to avoid Maratos effect, the nonmonotone strategy is employed. The analysis shows that, under standard conditions, the algorithm has global and superlinear convergence. Preliminary numerical experiments are conducted to show the effiency of the new method.
基金Supported by the National Natural Science Foundation of China(No.10671060)the Specialized Research Found for the Doctoral Program of Higher Education(No.20030532006)
文摘An efficient SQP algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the 1∞ exact penalty function through Armijo-type line search scheme. The algorithm is proved to be convergent globally under mild conditions.
