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Solving min-max problems and linear semi-infinite programs

✍ Scribed by S.-C. Fang; Soon-Yi Wu

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 309 KB
Volume: 32
Category: Article
ISSN: 0898-1221
DOI: 10.1016/0898-1221(96)00145-9

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✦ Synopsis

For a min-max problem in the form of minxEx maxtET {A(X)}, the nondi_fferentiability of the max function F(x) --maxtET {ft(x)} presents special difficulty in finding optimal solutions. We show that an entropic regularization procedure can provide a smooth approximation Fp(x) that uniformly converges to F(x) over X, as p tends to infinity. In this way, with p being sufficiently large, minimizing the smooth function Fp(x) over X provides a very accurate approximate solution to the min-max problem. When this approach is applied to solve linear semi-infinite programming problems, the previously proposed "unconstrained convex programming approach" is shown to be a special case.

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