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Volume 36, Issue 6
A Trust-Region Algorithm for Solving Mini-Max Problem

Bothina El-Sobky & Abdallah Abotahoun

DOI: 10.4208/jcm.1705-m2016-0735

J. Comp. Math., 36 (2018), pp. 776-791.

Published online: 2018-08

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  • Abstract

In this paper, we propose an algorithm for solving inequality constrained mini-max optimization problem. In this algorithm, an active set strategy is used together with multiplier method to convert the inequality constrained mini-max optimization problem into unconstrained optimization problem. A trust-region method is a well-accepted technique in constrained optimization to assure global convergence and is more robust when they deal with rounding errors. One of the advantages of trust-region method is that it does not require the objective function of the model to be convex. 

A global convergence analysis for the proposed algorithm is presented under some conditions. To show the efficiency of the algorithm numerical results for a number of test problems are reported.

  • Keywords

Mini-max problem, active-set, multiplier method, trust-region, global convergence.

  • AMS Subject Headings

90C30, 90B50, 65K05, 62C20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

bothinaelsobky@yahoo.com (Bothina El-Sobky)

tahoun44@yahoo.com (Abdallah Abotahoun)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-776, author = {El-Sobky , Bothina and Abotahoun , Abdallah}, title = {A Trust-Region Algorithm for Solving Mini-Max Problem}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {6}, pages = {776--791}, abstract = {

In this paper, we propose an algorithm for solving inequality constrained mini-max optimization problem. In this algorithm, an active set strategy is used together with multiplier method to convert the inequality constrained mini-max optimization problem into unconstrained optimization problem. A trust-region method is a well-accepted technique in constrained optimization to assure global convergence and is more robust when they deal with rounding errors. One of the advantages of trust-region method is that it does not require the objective function of the model to be convex. 

A global convergence analysis for the proposed algorithm is presented under some conditions. To show the efficiency of the algorithm numerical results for a number of test problems are reported.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1705-m2016-0735}, url = {http://global-sci.org/intro/article_detail/jcm/12602.html} }
TY - JOUR T1 - A Trust-Region Algorithm for Solving Mini-Max Problem AU - El-Sobky , Bothina AU - Abotahoun , Abdallah JO - Journal of Computational Mathematics VL - 6 SP - 776 EP - 791 PY - 2018 DA - 2018/08 SN - 36 DO - http://doi.org/10.4208/jcm.1705-m2016-0735 UR - https://global-sci.org/intro/article_detail/jcm/12602.html KW - Mini-max problem, active-set, multiplier method, trust-region, global convergence. AB -

In this paper, we propose an algorithm for solving inequality constrained mini-max optimization problem. In this algorithm, an active set strategy is used together with multiplier method to convert the inequality constrained mini-max optimization problem into unconstrained optimization problem. A trust-region method is a well-accepted technique in constrained optimization to assure global convergence and is more robust when they deal with rounding errors. One of the advantages of trust-region method is that it does not require the objective function of the model to be convex. 

A global convergence analysis for the proposed algorithm is presented under some conditions. To show the efficiency of the algorithm numerical results for a number of test problems are reported.

Bothina El-Sobky & Abdallah Abotahoun. (2020). A Trust-Region Algorithm for Solving Mini-Max Problem. Journal of Computational Mathematics. 36 (6). 776-791. doi:10.4208/jcm.1705-m2016-0735
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