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Entropy-Like Proximal Methods in Convex Programming

Alfredo N. Iusem, B. F. Svaiter and Marc Teboulle
Mathematics of Operations Research
Vol. 19, No. 4 (Nov., 1994), pp. 790-814
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3690314
Page Count: 25
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Entropy-Like Proximal Methods in Convex Programming
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Abstract

We study an extension of the proximal method for convex programming, where the quadratic regularization kernel is substituted by a class of convex statistical distances, called φ-divergences, which are typically entropy-like in form. After establishing several basic properties of these quasi-distances, we present a convergence analysis of the resulting entropy-like proximal algorithm. Applying this algorithm to the dual of a convex program, we recover a wide class of nonquadratic multiplier methods and prove their convergence.

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