A new perturbed smooth penalty function for inequality constrained optimization

Volume 23, Issue 1, pp 36--48 http://dx.doi.org/10.22436/jmcs.023.01.04

Publication Date: October 02, 2020 Submission Date: December 05, 2019 Revision Date: January 24, 2020 Accteptance Date: April 22, 2020

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Authors

Touna Yang - Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China. Nguyen Thanh Binh - Department of Education and Training Yen Bai, Yen Bai city 32000, Vietnam. Truong Minh Chinh - Viet Tri University of Industry, Viet Tri city 35000, Vietnam. Le Huu Tung - Viet Tri University of Industry, Viet Tri city 35000, Vietnam. Duong Thi Hoa - Yen Bai Teacher's Training College, Yen Bai city 32000, Vietnam.

Abstract

In this paper, we first propose a new smoothing approach to the nonsmooth penalty function for constrained optimization problems, and then show that an approximate optimal solution of the original problem can be obtained by solving an optimal solution of the smoothed optimization problem. Based on the perturbed smooth exact penalty function, we develop an algorithm respectively to finding an approximate optimal solution of the original constrained optimization problem and prove the convergence of the proposed algorithm. The effectiveness of the smoothed penalty function is illustrated through three examples, which show that the algorithm seems efficient.

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Keywords

• Exact penalty function
• inequality constrained optimization
• smoothing method
• optimal solution

MSC

•  90C30
•  65K05
•  57R12

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