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Operations Research Transactions >

2025 , Vol. 29 >Issue 4: 61 - 71

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.04.005

Research Article

An exact penalty approach to a cone constrained optimization problem

  • Qianqian CHI ,
  • Yuying ZHOU
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  • 1. School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China
    2. Laiwu Experimental School of Jinan, Jinan 250022, Shandong, China

Received date: 2022-09-03

  Online published: 2025-12-11

Copyright

, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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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

Cite this article

Qianqian CHI , Yuying ZHOU . An exact penalty approach to a cone constrained optimization problem[J]. Operations Research Transactions, 2025 , 29(4) : 61 -71 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.04.005

References

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.
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