On the entropic regularization method for solving min-max problems with applications |
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Authors: | Li Xing-Si Fang Shu-Cherng |
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Institution: | (1) Research Institute of Engineering Mechanics, Dalian University of Technology, 116024 Dalian, People's Republic of China;(2) Operations Research and Industrial Engineering, North Carolina State University, 27695-7913 Raleigh, NC, USA |
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Abstract: | Consider a min-max problem in the form of min
x X
max1 i m
{f
i
(x)}. It is well-known that the non-differentiability of the max functionF(x) max1 i m
{f
i
(x)} presents difficulty in finding an optimal solution. An entropic regularization procedure provides a smooth approximationF
p(x) that uniformly converges toF(x) overX with a difference bounded by ln(m)/p, forp > 0. In this way, withp being sufficiently large, minimizing the smooth functionF
p(x) overX provides a very accurate solution to the min-max problem. The same procedure can be applied to solve systems of inequalities, linear programming problems, and constrained min-max problems.This research work was supported in part by the 1995 NCSC-Cray Research Grant and the National Textile Center Research Grant S95-2. |
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Keywords: | Min-Max Problem Linear and Nonlinear Programming Entropy Optimization Principles |
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