On the entropic regularization method for solving min-max problems with applications

Xing-Si Li and Shu-Cherng Fang ()

Mathematical Methods of Operations Research, 1997, vol. 46, issue 1, 119-130

Abstract: Consider a min-max problem in the form of min xεX max 1≤i≤m {f i (x)}. It is well-known that the non-differentiability of the max functionF(x) ≡ max 1≤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. Copyright Physica-Verlag 1997

Keywords: Min-Max Problem; Linear and Nonlinear Programming; Entropy Optimization Principles (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/BF01199466

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