Partial Exactness for the Penalty Function of Biconvex Programming
Biconvex programming (or inequality constrained biconvex optimization) is an important model in solving many engineering optimization problems in areas like machine learning and signal and information processing. In this paper, the partial exactness of the partial optimum for the penalty function of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/2/132 |
| _version_ | 1797409023772852224 |
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| author | Min Jiang Zhiqing Meng Rui Shen |
| author_facet | Min Jiang Zhiqing Meng Rui Shen |
| author_sort | Min Jiang |
| collection | DOAJ |
| description | Biconvex programming (or inequality constrained biconvex optimization) is an important model in solving many engineering optimization problems in areas like machine learning and signal and information processing. In this paper, the partial exactness of the partial optimum for the penalty function of biconvex programming is studied. The penalty function is partially exact if the partial Karush–Kuhn–Tucker (KKT) condition is true. The sufficient and necessary partially local stability condition used to determine whether the penalty function is partially exact for a partial optimum solution is also proven. Based on the penalty function, an algorithm is presented for finding a partial optimum solution to an inequality constrained biconvex optimization, and its convergence is proven under some conditions. |
| first_indexed | 2024-03-09T04:08:19Z |
| format | Article |
| id | doaj.art-05113ea1e98044be8ac25e8428687094 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T04:08:19Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-05113ea1e98044be8ac25e84286870942023-12-03T14:03:05ZengMDPI AGEntropy1099-43002021-01-0123213210.3390/e23020132Partial Exactness for the Penalty Function of Biconvex ProgrammingMin Jiang0Zhiqing Meng1Rui Shen2School of Management, Zhejiang University of Technology, Hangzhou 310023, ChinaSchool of Management, Zhejiang University of Technology, Hangzhou 310023, ChinaSchool of Economics, Zhejiang University of Technology, Hangzhou 310023, ChinaBiconvex programming (or inequality constrained biconvex optimization) is an important model in solving many engineering optimization problems in areas like machine learning and signal and information processing. In this paper, the partial exactness of the partial optimum for the penalty function of biconvex programming is studied. The penalty function is partially exact if the partial Karush–Kuhn–Tucker (KKT) condition is true. The sufficient and necessary partially local stability condition used to determine whether the penalty function is partially exact for a partial optimum solution is also proven. Based on the penalty function, an algorithm is presented for finding a partial optimum solution to an inequality constrained biconvex optimization, and its convergence is proven under some conditions.https://www.mdpi.com/1099-4300/23/2/132biconvex programmingpartial optimumpartially exact penalty functionpartial exactnesspartial local stability |
| spellingShingle | Min Jiang Zhiqing Meng Rui Shen Partial Exactness for the Penalty Function of Biconvex Programming Entropy biconvex programming partial optimum partially exact penalty function partial exactness partial local stability |
| title | Partial Exactness for the Penalty Function of Biconvex Programming |
| title_full | Partial Exactness for the Penalty Function of Biconvex Programming |
| title_fullStr | Partial Exactness for the Penalty Function of Biconvex Programming |
| title_full_unstemmed | Partial Exactness for the Penalty Function of Biconvex Programming |
| title_short | Partial Exactness for the Penalty Function of Biconvex Programming |
| title_sort | partial exactness for the penalty function of biconvex programming |
| topic | biconvex programming partial optimum partially exact penalty function partial exactness partial local stability |
| url | https://www.mdpi.com/1099-4300/23/2/132 |
| work_keys_str_mv | AT minjiang partialexactnessforthepenaltyfunctionofbiconvexprogramming AT zhiqingmeng partialexactnessforthepenaltyfunctionofbiconvexprogramming AT ruishen partialexactnessforthepenaltyfunctionofbiconvexprogramming |