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Math. Comput. Appl. 2017, 22(2), 31; doi:10.3390/mca22020031

A New Smoothing Nonlinear Penalty Function for Constrained Optimization

1
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2
Department of Mathematics, Shanghai University, Shanghai 200444, China
3
Yen Bai Teacher’s Training College, Yen Bai City 320000, Vietnam
4
Department of Education and Training Yen Bai, Yen Bai City 320000, Vietnam
*
Author to whom correspondence should be addressed.
Academic Editor: Fazal M. Mahomed
Received: 5 November 2016 / Revised: 29 March 2017 / Accepted: 4 April 2017 / Published: 12 April 2017
View Full-Text   |   Download PDF [777 KB, uploaded 12 April 2017]   |  

Abstract

In this study, a new smoothing nonlinear penalty function for constrained optimization problems is presented. It is proved that the optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, we develop an algorithm for finding an optimal solution of the optimization problems with inequality constraints. We further discuss the convergence of this algorithm and test this algorithm with three numerical examples. The numerical examples show that the proposed algorithm is feasible and effective for solving some nonlinear constrained optimization problems. View Full-Text
Keywords: penalty function; smoothing method; constrained optimization penalty function; smoothing method; constrained optimization
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MDPI and ACS Style

Yang, T.; Binh, N.T.; Thang, T.M.; Hoa, D.T. A New Smoothing Nonlinear Penalty Function for Constrained Optimization. Math. Comput. Appl. 2017, 22, 31.

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