Perturbed smoothing approach to the lower order exact penalty functions for nonlinear inequality constrained optimization

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Published: Mar 30, 2018
DOI: https://doi.org/10.5556/j.tkjm.50.2019.2625
Keywords:
nonlinear constrained optimization exact penalty function smoothing method optimal solution

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Binh Thanh Nguyen
Yanqin Bai
Xin Yan
Touna Yang

Abstract

In this paper, we propose two new smoothing approximation to the lower order exact penalty functions for nonlinear optimization problems with inequality constraints. Error estimations between smoothed penalty function and nonsmooth penalty function are investigated. By using these new smooth penalty functions, a nonlinear optimization problem with inequality constraints is converted into a sequence of minimizations of continuously differentiable function. Then based on each of the smoothed penalty functions, we develop an algorithm respectively to finding an approximate optimal solution of the original constrained optimization problem and prove the convergence of the proposed algorithms. The effectiveness of the smoothed penalty functions is illustrated through three examples, which show that the algorithm seems efficient.

Article Details

How to Cite
Nguyen, B. T., Bai, Y., Yan, X., & Yang, T. (2018). Perturbed smoothing approach to the lower order exact penalty functions for nonlinear inequality constrained optimization. Tamkang Journal of Mathematics, 50(1), 37–60. https://doi.org/10.5556/j.tkjm.50.2019.2625
Issue
Vol. 50 No. 1 (2019)
Section
Papers
Author Biographies

Binh Thanh Nguyen

Department of Mathematics, Shanghai University, Shanghai 200444, China. and YenBai Teacher’s Training College, Yen Bai city, Vietnam.

Yanqin Bai

Department ofMathematics, Shanghai University, Shanghai 200444, China.

Xin Yan

School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China.

Touna Yang

School ofMathematical Sciences, Dalian University of Technology, Dalian 116024, China.

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