05057153

j

05057153 Jiang, Yuxi Pan, Shaohua LI, Xingsi Relationship between entropy regularization method and exponential penalty method. Numer. Math., Nanjing 27, No. 4, 355-362 (2005). 2005 Nanjing University, Department of Mathematics, Nanjing ZH numerical examples duality relationship finite min-max problem Zbl 0886.90133 Summary: {\it X.-S. Li} and {\it S.-C. Fang} [Math. Methods Oper. Res. 46, No. 1, 119--130 (1997; Zbl 0886.90133)] have derived two smooth functions uniformly approximating the max-type function for the finite min-max problem through an entropy regularization method. Here, we present an alternative derivation of these smooth functions by means of the conventional exponential (multiplier) penalty method, whereby exploring a duality relalionship between these two approaches. We also give a rigorous proof for this duality property with use of the Fenchel duality theorem in convex analysis. It is hoped that this paper would help to correctly understand the entropy regularization method and the proper use of corresponding smooth functions.