The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems
We adopt the alternating direction search pattern method to solve the equality and inequality constrained nonlinear optimization problems. Firstly, a new augmented Lagrangian function with a nonlinear complementarity function is proposed to transform the original constrained problem into a new uncon...
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| Format: | Article |
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/8/1863 |
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| author | Aifen Feng Xiaogai Chang Youlin Shang Jingya Fan |
| author_facet | Aifen Feng Xiaogai Chang Youlin Shang Jingya Fan |
| author_sort | Aifen Feng |
| collection | DOAJ |
| description | We adopt the alternating direction search pattern method to solve the equality and inequality constrained nonlinear optimization problems. Firstly, a new augmented Lagrangian function with a nonlinear complementarity function is proposed to transform the original constrained problem into a new unconstrained problem. Under appropriate conditions, it has been proven that there is a 1-1 correspondence between the local and global optimal solutions of the new unconstrained problem and the original constrained problem. In this way, the optimal solution of the original problem can be obtained by solving the new unconstrained optimization problem. Furthermore, based on the characteristics of the new problem, the alternating direction pattern search method was designed and its convergence was demonstrated. Numerical experiments were implemented to illustrate the availability of the new augmented Lagrangian function and the algorithm. |
| first_indexed | 2024-03-11T04:47:01Z |
| format | Article |
| id | doaj.art-bfceb48ecb7e4078982798fe1816248e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:47:01Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bfceb48ecb7e4078982798fe1816248e2023-11-17T20:17:39ZengMDPI AGMathematics2227-73902023-04-01118186310.3390/math11081863The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization ProblemsAifen Feng0Xiaogai Chang1Youlin Shang2Jingya Fan3School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaWe adopt the alternating direction search pattern method to solve the equality and inequality constrained nonlinear optimization problems. Firstly, a new augmented Lagrangian function with a nonlinear complementarity function is proposed to transform the original constrained problem into a new unconstrained problem. Under appropriate conditions, it has been proven that there is a 1-1 correspondence between the local and global optimal solutions of the new unconstrained problem and the original constrained problem. In this way, the optimal solution of the original problem can be obtained by solving the new unconstrained optimization problem. Furthermore, based on the characteristics of the new problem, the alternating direction pattern search method was designed and its convergence was demonstrated. Numerical experiments were implemented to illustrate the availability of the new augmented Lagrangian function and the algorithm.https://www.mdpi.com/2227-7390/11/8/1863nonlinear programmingnonlinear complementarity functionalternating direction search pattern method |
| spellingShingle | Aifen Feng Xiaogai Chang Youlin Shang Jingya Fan The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems Mathematics nonlinear programming nonlinear complementarity function alternating direction search pattern method |
| title | The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems |
| title_full | The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems |
| title_fullStr | The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems |
| title_full_unstemmed | The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems |
| title_short | The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems |
| title_sort | alternating direction search pattern method for solving constrained nonlinear optimization problems |
| topic | nonlinear programming nonlinear complementarity function alternating direction search pattern method |
| url | https://www.mdpi.com/2227-7390/11/8/1863 |
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