Proximal Point Methods for Quasiconvex and Convex Functions With Bregman Distances

Erik Alex Papa Quiroz (erikcos.ufrj.br)
Paulo Roberto Oliveira (poliveircos.ufrj.br)

Abstract: This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, applied to a class of quasiconvex problems. Finally, we give some examples of Bregman distances in non-Euclidean spaces.

Keywords: Proximal point algorithms, Hadamard manifolds,

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

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Entry Submitted: 04/25/2006
Entry Accepted: 04/25/2006
Entry Last Modified: 04/25/2006

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