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

被引：0

作者：

Zhang, Lili ^{[1
]}

Li, Jianyu ^{[2
]}

Li, Xingsi ^{[3
]}

机构：

[1] Dalian Univ Technol, Dept Appl Math, Dalian, Peoples R China

[2] Tianjin Univ Sci & Technol, Sch Mech Engn, Tianjin, Peoples R China

[3] Dalian Univ Technol, Dept Engn Mech, State Key Lab Struct Anal Ind Equipment, Dalian, Peoples R China

来源：

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2010年 / 3卷 / 01期

基金：

中国国家自然科学基金;

关键词：

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

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：98 / 106

页数：9

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