- Title
- A New Objective Penalty Function Approach for Solving Constrained Minimax Problems
- Creator
- Li, Jueyou; Wu, Zhiyou; Long, Qiang
- Date
- 2014
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/59177
- Identifier
- vital:5878
- Identifier
-
https://doi.org/10.1007/s40305-014-0041-3
- Identifier
- ISSN:2194-6698
- Abstract
- In this paper, a new objective penalty function approach is proposed for solving minimax programming problems with equality and inequality constraints. This new objective penalty function combines the objective penalty and constraint penalty. By the new objective penalty function, a constrained minimax problem is converted to minimizations of a sequence of continuously differentiable functions with a simple box constraint. One can thus apply any efficient gradient minimization methods to solve the minimizations with box constraint at each step of the sequence. Some relationships between the original constrained minimax problem and the corresponding minimization problems with box constraint are established. Based on these results, an algorithm for finding a global solution of the constrained minimax problems is proposed by integrating the particular structure of minimax problems and its global convergence is proved under some conditions. Furthermore, an algorithm is developed for finding a local solution of the constrained minimax problems, with its convergence proved under certain conditions. Preliminary results of numerical experiments with well-known test problems show that satisfactorily approximate solutions for some constrained minimax problems can be obtained.
- Publisher
- Springer, Berlin
- Relation
- Journal of the Operations Research Society of China Vol. 2, no. 1 (March 2014 2014), p. 93-108
- Rights
- © 2014 Operations Research Society of China, Periodicals Agency of Shanghai University, and Springer-Verlag Berlin Heidelberg.
- Rights
- This metadata is freely available under a CCO license
- Subject
- Approximate solution; Constrained minimization; Minimax problem; Objective penalty function
- Reviewed
- Hits: 676
- Visitors: 670
- Downloads: 2
| Thumbnail | File | Description | Size | Format |
|---|