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Operations Research Transactions >

2024 , Vol. 28 >Issue 4: 57 - 65

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2024.04.005

Partial exactness of penalty function of multi-convex programming

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  • 1. School of Management, Zhejiang University of Technology, Hangzhou 310023, Zhejiang, China

Received date: 2021-07-09

  Online published: 2024-12-20

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, 2024, All rights reserved, without authorization
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Abstract

Multi-convex programming(MCP) is an important model in solving many engineering optimization problems in areas like machine learning and signal and information processing. In this paper, some new concepts of partial optimum, partial KKT condition, partial KKT ponit, partial Slater constraint qualification, partial exactness and partial stableness for the penalty function of multi-convex programming are defined. Under the partial Slater constraint qualification, a partial optimum of MCP is proved to be equivalent to partial KKT condition of MCP. The partial exactness of MCP is proved to be equivalent to partial KKT condition of MCP. The partial exactness of MCP is proved to be equivalent to partial stableness of MCP. These results are important for studying the exact penalty function of multi convex programming.

Key words： multi-convex programming; partial optimum; partial KKT condition; partial exactness; partial stableness

Cite this article

Yichen LAI, Zhiqing MENG . Partial exactness of penalty function of multi-convex programming[J]. Operations Research Transactions, 2024 , 28(4) : 57 -65 . DOI: 10.15960/j.cnki.issn.1007-6093.2024.04.005

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