多凸规划罚函数的部分精确性研究

doi:10.15960/j.cnki.issn.1007-6093.2024.04.005

运筹学学报（中英文） ›› 2024, Vol. 28 ›› Issue (4): 57-65.doi: 10.15960/j.cnki.issn.1007-6093.2024.04.005

多凸规划罚函数的部分精确性研究

来翊晨¹, 孟志青¹^,*()

1. 浙江工业大学管理学院, 浙江杭州 310023

收稿日期:2021-07-09 出版日期:2024-12-15 发布日期:2024-12-20
通讯作者: 孟志青 E-mail:mengzhiqing@zjut.edu.cn
基金资助:
国家自然科学基金面上项目(11871434);浙江省自然科学基金(LY18A010031)

Partial exactness of penalty function of multi-convex programming

Yichen LAI¹, Zhiqing MENG¹^,*()

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

Received:2021-07-09 Online:2024-12-15 Published:2024-12-20
Contact: Zhiqing MENG E-mail:mengzhiqing@zjut.edu.cn

摘要/Abstract

摘要：

多凸规划是解决机器学习、信号与信息处理等领域中许多工程优化问题的重要模型。本文定义了多凸规划罚函数的部分最优解、部分KKT条件、部分KKT点、部分Slater约束条件、部分精确性和部分稳定性等新概念。在部分Slater约束条件下, 证明了多凸规划的部分最优解等价于部分KKT条件, 并证明了多凸规划的部分精确性等价于部分KKT条件和多凸规划的部分精确性等价于部分稳定性等结果。这些结果对于研究多凸规划的精确罚函数具有重要意义。

关键词: 多凸规划, 部分最优解, 部分KKT条件, 部分精确性, 部分稳定性

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

中图分类号:

O122.2

来翊晨, 孟志青. 多凸规划罚函数的部分精确性研究[J]. 运筹学学报（中英文）, 2024, 28(4): 57-65.

Yichen LAI, Zhiqing MENG. Partial exactness of penalty function of multi-convex programming[J]. Operations Research Transactions, 2024, 28(4): 57-65.

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多凸规划罚函数的部分精确性研究

Partial exactness of penalty function of multi-convex programming

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