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

• • 上一篇

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 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(No.11971339)

An exact penalty approach to a cone constrained optimization problem

CHI Qianqian^1,2, ZHOU Yuying^1,†

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 Published:2025-12-11

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, $\mu$ 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, $\mu$ 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.

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

参考文献

[1] Eremin I I. The penalty method in convex programming [J]. Soviet Mathematics-Doklady, 1966, 8: 459-462.
[2] Zangwill W I. Nonlinear programming via penalty functions [J]. Management Science, 1967, 13: 344-358.
[3] Han S P, Mangasarian O L. Exact penalty function in nonlinear programming [J]. Mathematical Programming, 1979, 17: 251-269.
[4] Auslender A. Penalty and barrier methods: A unified framework [J]. SIAM Journal on Optimization, 1999, 10: 211-230.
[5] Boukari D, Fiacco A V. Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993[J]. Optimization, 1995, 32: 301-334.
[6] Burke J V. An exact penalization viewpoint of constrained optimization [J]. SIAM Journal on Control Optimization, 1991, 29: 968-998.
[7] Demyanov V F. Exact penalty functions and problems of the calculus of variations [J]. Automation and Remote Control, 2004, 65: 280-290.
[8] Di Pillo G, Grippo L. Exact penalty functions in constrained optimization [J]. SIAM Journal on Control Optimization, 1989, 27: 1333-1360.
[9] Zaslavski A J. An estimation of exact penalty for infinite-dimensional inequality-constrained minimization problem [J]. Set-valued and Variational Analysis, 2011, 19: 385-398.
[10] Carl S. Existence and extremal solutions of parabolic variational-hemivariational inequalities [J]. Monatshefte Für Mathematik, 2013, 172: 29-54.
[11] Zaslavski A J. An approximate exact penalty in constrained vector optimization on metric spaces [J]. Journal of Optimization Theory and Applications, 2014, 162: 649-664.
[12] Zhou Y Y, Wang S. Yang X Q. A penalty approximation method for a semilinear parabolic double obstacle problem [J]. Journal of Global Optimization, 2014, 60: 531-550.
[13] Wang S. An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem [J]. Applied Mathematical Modelling, 2018, 58: 217-228.
[14] Duan Y R, Wang S. Zhou Y Y. A power penalty approach to a mixed quasilinear elliptic complementarity problem [J]. Journal of Global Optimization, 2021, 81: 901-918.
[15] Zhang K, Yang X Q, Wang S. Solution method for discrete double obstacle problems based on a power penalty approach [J]. Journal of Industrial and Management Optimization, 2022, 18: 1261-1274.
[16] Ekeland I. On the variational principle [J]. Journal of Mathematical Analysis and Applications, 1974, 47: 324-353.

锥约束优化问题的精确罚逼近

An exact penalty approach to a cone constrained optimization problem

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	李鑫怡, 高英, 赵春杰. 定向距离函数的光滑化方法及其应用[J]. 运筹学学报（中英文）, 2024, 28(2): 117-130.
[2]	姜波. 非负正交约束优化问题的理论、算法及应用[J]. 运筹学学报, 2023, 27(4): 136-152.
[3]	汪文意, 高英, 刘芙萍. co-radiant集的等价表示及其在向量优化问题中的应用[J]. 运筹学学报, 2021, 25(2): 135-143.
[4]	陈瑞婷, 徐智会, 高英. 拟凸多目标优化问题近似解的最优性条件[J]. 运筹学学报, 2019, 23(1): 35-44.
[5]	连淑君，唐加会，杜爱华. 带等式约束的光滑优化问题的一类新的精确罚函数[J]. 运筹学学报, 2018, 22(4): 108-116.
[6]	杨新民, 赵克全. 向量优化问题的近似解研究[J]. 运筹学学报, 2017, 21(4): 1-18.
[7]	郑跃, 庄道元, 万仲平. 求解弱线性双层规划问题的一种全局优化方法[J]. 运筹学学报, 2017, 21(3): 86-94.
[8]	连淑君, 杜爱华, 唐加会. 等式约束优化问题的一类新的简单光滑精确罚函数[J]. 运筹学学报, 2017, 21(1): 33-43.
[9]	王长钰, 赵文玲. 约束优化问题的一类光滑罚算法的全局收敛特性[J]. 运筹学学报, 2015, 19(3): 151-160.
[10]	孟志青, 沈瑞, 徐新生, 蒋敏. 一种双层规划的光滑化目标罚函数算法[J]. 运筹学学报, 2015, 19(3): 26-33.
[11]	吕一兵, 万仲平. 线性半向量二层规划问题的全局优化方法[J]. 运筹学学报, 2015, 19(2): 29-36.
[12]	孟志青，高嵩 . 非线性约束优化的光滑化平方根罚函数[J]. 运筹学学报, 2013, 17(2): 70-80.
[13]	高英. 多面体集下多目标优化问题近似解的若干性质[J]. 运筹学学报, 2013, 17(2): 48-52.
[14]	白富生, 罗晓艳. 基于二次函数光滑化逼近的修正低阶罚函数[J]. 运筹学学报, 2012, 16(2): 9-22.
[15]	连淑君. 不等式约束优化问题的低阶精确罚函数的光滑化算法[J]. 运筹学学报, 2012, 16(2): 51-64.