A new adaptive method to nonlinear semi-infinite programming

Ke Su; Yumeng Lin; Chun Xu

doi:10.3934/jimo.2021012

Article Contents

2022, Volume 18, Issue 2: 1133-1144. Doi: 10.3934/jimo.2021012

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A new adaptive method to nonlinear semi-infinite programming

College of Mathematics and Information Science, Hebei University, Hebei Key Laboratory of Machine Learning and Computational Intelligence, Baoding 071002, China

$ ^{\star} $ Corresponding author: Yumeng Lin
$ ^{\star} $ Corresponding author: Yumeng Lin

Received: February 29, 2020

Revised: September 30, 2020

Early access: December 2020

Published: March 2022

$ ^* $ The first author is supported by the National Natural Science Foundation of China (No. 11101115), the Natural Science Foundation of Hebei Province (grant No. A2018201172), the Key Research Foundation of Education Bureau of Hebei Province (grant No. ZD2015069), the graduate student Innovation ability training project of Hebei University (grant number hbu2020ss043)

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Abstract

In this paper, we propose a new adaptive method for solving nonlinear semi-infinite programming(SIP). In the presented method, the continuous infinite inequality constraints are transformed into equivalent equality constraints in integral form. Based on penalty method and trust region strategy, we propose a modified quadratic subproblem, in which an adaptive parameter is considered. The acceptable criterion of the trial point is adjustable according to the value of this adaptive parameter and the improvements that made by the current iteration. Compared with the existing methods, our method is more flexible. Under some reasonable conditions, the convergent properties of the proposed algorithm are proved. The numerical results are reported in the end.

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Mathematics Subject Classification: Primary: 90C30; Secondary: 65K05.

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Table 1. comparison between Algorithm 1 and algorithm in MATLAB

problem	Algorithm 1				Algorithm in MATLAB
problem	Iter	CPU	$ f(x^{\ast}) $	$ I_{g} $	Iter	CPU	$ f(x^{\ast}) $	$ I_{g} $
$ 1 $	14	0.1711	1.8348	25	38	0.1835	2.1126	202
$ 2 $	25	0.4832	5.3257	31	39	0.7644	5.1293	303
$ 3 $	33	0.3198	0.1944	43	8	0.5304	0.1945	38
$ 4 $	26	2.5901	10.7224	27	70	5.9672	11.2252	1010

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