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

Lili Zhang, Jianyu Li, Xingsi Li

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.

Keywords

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

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