On the Cross-Entropic Regularization Method for Solving Min-Max Problems

Authors

  • Lili Zhang Department of Applied Mathematics, Dalian University of Technology, Dalian, P.R. China
  • Jianyu Li School of Mechanical Engineering,Tianjin University of Science and Technology
  • Xingsi Li State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology

Keywords:

Min-Max Problem, Cross-Entropic Regularization, Smooth Approximation, Subgradient, Condition Number

Abstract

A smoothing method of multipliers which is a natural result of cross-entropic regularization for min-max problems is analyzed. As a smoothing technique, we first show how the smooth approximation yields the first order information on the behavior of max function. Then under suitable assumptions, some basic properties including the Hessian are given. At last, the condition number is analyzed, and the results reveal that the smoothing method of multipliers is stable for any fixed smoothing parameter.

Author Biographies

  • Lili Zhang, Department of Applied Mathematics, Dalian University of Technology, Dalian, P.R. China
    Ph.D. student,  Department of Applied Mathematics, Dalian University of Technology
  • Jianyu Li, School of Mechanical Engineering,Tianjin University of Science and Technology
    Associate Professor, School of Mechanical Engineering,Tianjin University of Science and Technology,Tianjin, P. R. China
  • Xingsi Li, State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology
    Professor, State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, P. R. China,

Downloads

Published

2009-12-16

Issue

Vol. 3 No. 1: (January 2010)

Section

Optimization

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

On the Cross-Entropic Regularization Method for Solving Min-Max Problems. (2009). European Journal of Pure and Applied Mathematics, 3(1), 98-106. https://www.ejpam.com/index.php/ejpam/article/view/214