锥约束优化问题的精确罚逼近

doi:10.15960/j.cnki.issn.1007-6093.2025.04.005

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (4): 61-71.doi: 10.15960/j.cnki.issn.1007-6093.2025.04.005

锥约束优化问题的精确罚逼近

池倩倩¹^,², 周育英¹^,*()

1. 苏州大学数学科学学院, 江苏苏州 215006
2. 济南市莱芜实验学校, 山东济南 250022

收稿日期:2022-09-03 出版日期:2025-12-15 发布日期:2025-12-11
通讯作者: 周育英 E-mail:yuyingz@suda.edu.cn
基金资助:
国家自然科学基金(11971339)

An exact penalty approach to a cone constrained optimization problem

Qianqian CHI¹^,², Yuying ZHOU¹^,*()

1. School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China
2. Laiwu Experimental School of Jinan, Jinan 250022, Shandong, China

Received:2022-09-03 Online:2025-12-15 Published:2025-12-11
Contact: Yuying ZHOU E-mail:yuyingz@suda.edu.cn

摘要/Abstract

摘要：

本文利用罚逼近的方法研究在完备度量空间中的锥约束优化问题。在不需要假设目标函数强制及约束函数为凸函数的情况下, 利用一类$\mu$函数的性质、Ekeland变分原理以及一些新的技巧, 证明存在一个罚因子, 其对应的无约束罚问题存在近似解, 从而得到原锥约束优化问题近似解的存在性。

关键词: 锥约束优化, 罚函数, μ函数, 近似解

Abstract:

A penalty approach method has been used to deal with a cone constrained minimization problem on complete metric spaces in this paper. By exploring Ekeland's variational principle, the property of $\mu$-function and some new technique, approximate solutions of the unconstrained penalized problem for some penalty parameter have been established, and then approximate solutions of the cone constrained optimization have been obtained without assuming that the constrained function is convex and the objective function satisfies the coercive condition.

Key words: cone constrained optimization, penalty function, μ function, approximate solutions

中图分类号:

O221.2

池倩倩, 周育英. 锥约束优化问题的精确罚逼近[J]. 运筹学学报（中英文）, 2025, 29(4): 61-71.

Qianqian CHI, Yuying ZHOU. An exact penalty approach to a cone constrained optimization problem[J]. Operations Research Transactions, 2025, 29(4): 61-71.

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锥约束优化问题的精确罚逼近

An exact penalty approach to a cone constrained optimization problem

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