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Entropy-like proximal methods in convex programming. (English) Zbl 0821.90092

Summary: 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 \(\varphi\)-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.

MSC:

90C25 Convex programming
90C30 Nonlinear programming
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