Objective penalty function method for nonlinear programming with inequality constraints
This paper presents a novel nonsmooth objective penalty function for inequality constrained optimization problems. A modified flattened aggregate function, which is a smooth approximation of the max-value function, is discussed. Then, the smooth objective penalty function that contains the flattened...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-11-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241602 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590748788195328 |
|---|---|
| author | Zhuolin Yan Xiaowei Jiang Siyao Wang |
| author_facet | Zhuolin Yan Xiaowei Jiang Siyao Wang |
| author_sort | Zhuolin Yan |
| collection | DOAJ |
| description | This paper presents a novel nonsmooth objective penalty function for inequality constrained optimization problems. A modified flattened aggregate function, which is a smooth approximation of the max-value function, is discussed. Then, the smooth objective penalty function that contains the flattened aggregate function is proposed, and the exactness of the new function is studied. Based on this, an objective penalty function algorithm is proposed and its convergence is proven under mild conditions. Because of the flattened aggregate function, the gradient computation can usually be greatly reduced for problems with many constraints. Numerical experiments are included to illustrate the efficiency of the new algorithm through a series of numerical examples, especially for solving problems with many constraints. |
| format | Article |
| id | doaj-art-6a4af6329eec4db5b6230829b2520632 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-6a4af6329eec4db5b6230829b25206322025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912335723359010.3934/math.20241602Objective penalty function method for nonlinear programming with inequality constraintsZhuolin Yan0Xiaowei Jiang1Siyao Wang2School of Mathematics and Statistics, Beihua University, Jilin, Jilin, 132013, ChinaSchool of Mathematics and Statistics, Beihua University, Jilin, Jilin, 132013, ChinaSchool of Mathematics and Statistics, Beihua University, Jilin, Jilin, 132013, ChinaThis paper presents a novel nonsmooth objective penalty function for inequality constrained optimization problems. A modified flattened aggregate function, which is a smooth approximation of the max-value function, is discussed. Then, the smooth objective penalty function that contains the flattened aggregate function is proposed, and the exactness of the new function is studied. Based on this, an objective penalty function algorithm is proposed and its convergence is proven under mild conditions. Because of the flattened aggregate function, the gradient computation can usually be greatly reduced for problems with many constraints. Numerical experiments are included to illustrate the efficiency of the new algorithm through a series of numerical examples, especially for solving problems with many constraints.https://www.aimspress.com/article/doi/10.3934/math.20241602nonlinear programminginequality constraintexact penalty functionobjective penalty functionflattened aggregate function |
| spellingShingle | Zhuolin Yan Xiaowei Jiang Siyao Wang Objective penalty function method for nonlinear programming with inequality constraints AIMS Mathematics nonlinear programming inequality constraint exact penalty function objective penalty function flattened aggregate function |
| title | Objective penalty function method for nonlinear programming with inequality constraints |
| title_full | Objective penalty function method for nonlinear programming with inequality constraints |
| title_fullStr | Objective penalty function method for nonlinear programming with inequality constraints |
| title_full_unstemmed | Objective penalty function method for nonlinear programming with inequality constraints |
| title_short | Objective penalty function method for nonlinear programming with inequality constraints |
| title_sort | objective penalty function method for nonlinear programming with inequality constraints |
| topic | nonlinear programming inequality constraint exact penalty function objective penalty function flattened aggregate function |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241602 |
| work_keys_str_mv | AT zhuolinyan objectivepenaltyfunctionmethodfornonlinearprogrammingwithinequalityconstraints AT xiaoweijiang objectivepenaltyfunctionmethodfornonlinearprogrammingwithinequalityconstraints AT siyaowang objectivepenaltyfunctionmethodfornonlinearprogrammingwithinequalityconstraints |