A new filter QP-free method for the nonlinear inequality constrained optimization problem
Abstract In this paper, a filter QP-free infeasible method with nonmonotone line search is proposed for minimizing a smooth optimization problem with smooth inequality constraints. This proposed method is based on the solution of nonsmooth equations, which are obtained by the Lagrangian multiplier m...
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Online Access: | http://link.springer.com/article/10.1186/s13660-018-1851-3 |
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doaj-b182f4811fbd4f89b11816736d75e0be2020-11-25T01:20:45ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-10-012018111410.1186/s13660-018-1851-3A new filter QP-free method for the nonlinear inequality constrained optimization problemYoulin Shang0Zheng-Fen Jin1Dingguo Pu2School of Mathematics and Statistics, Henan University of Science and TechnologySchool of Mathematics and Statistics, Henan University of Science and TechnologyDepartment of Mathematics, Tongji UniversityAbstract In this paper, a filter QP-free infeasible method with nonmonotone line search is proposed for minimizing a smooth optimization problem with smooth inequality constraints. This proposed method is based on the solution of nonsmooth equations, which are obtained by the Lagrangian multiplier method and the function of the nonlinear complementarity problem for the Karush–Kuhn–Tucker optimality conditions. Especially, each iteration of this method can be viewed as a perturbation of a Newton or quasi-Newton iteration on both the primal and dual variables for the solution of the Karush–Kuhn–Tucker optimality conditions. What is more, it is considered to use the function of the nonlinear complementarity problem in the filter, which makes the proposed algorithm avoid the incompatibility. Then the global convergence of the proposed method is given. And under some mild conditions, the superlinear convergence rate can be obtained. Finally, some preliminary numerical results are shown to illustrate that the proposed filter QP-free infeasible method is quite promising.http://link.springer.com/article/10.1186/s13660-018-1851-3Nonlinear constrained optimizationFilter methodQP-free methodNonmonotone line search |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Youlin Shang Zheng-Fen Jin Dingguo Pu |
spellingShingle |
Youlin Shang Zheng-Fen Jin Dingguo Pu A new filter QP-free method for the nonlinear inequality constrained optimization problem Journal of Inequalities and Applications Nonlinear constrained optimization Filter method QP-free method Nonmonotone line search |
author_facet |
Youlin Shang Zheng-Fen Jin Dingguo Pu |
author_sort |
Youlin Shang |
title |
A new filter QP-free method for the nonlinear inequality constrained optimization problem |
title_short |
A new filter QP-free method for the nonlinear inequality constrained optimization problem |
title_full |
A new filter QP-free method for the nonlinear inequality constrained optimization problem |
title_fullStr |
A new filter QP-free method for the nonlinear inequality constrained optimization problem |
title_full_unstemmed |
A new filter QP-free method for the nonlinear inequality constrained optimization problem |
title_sort |
new filter qp-free method for the nonlinear inequality constrained optimization problem |
publisher |
SpringerOpen |
series |
Journal of Inequalities and Applications |
issn |
1029-242X |
publishDate |
2018-10-01 |
description |
Abstract In this paper, a filter QP-free infeasible method with nonmonotone line search is proposed for minimizing a smooth optimization problem with smooth inequality constraints. This proposed method is based on the solution of nonsmooth equations, which are obtained by the Lagrangian multiplier method and the function of the nonlinear complementarity problem for the Karush–Kuhn–Tucker optimality conditions. Especially, each iteration of this method can be viewed as a perturbation of a Newton or quasi-Newton iteration on both the primal and dual variables for the solution of the Karush–Kuhn–Tucker optimality conditions. What is more, it is considered to use the function of the nonlinear complementarity problem in the filter, which makes the proposed algorithm avoid the incompatibility. Then the global convergence of the proposed method is given. And under some mild conditions, the superlinear convergence rate can be obtained. Finally, some preliminary numerical results are shown to illustrate that the proposed filter QP-free infeasible method is quite promising. |
topic |
Nonlinear constrained optimization Filter method QP-free method Nonmonotone line search |
url |
http://link.springer.com/article/10.1186/s13660-018-1851-3 |
work_keys_str_mv |
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