A Proximal Point Algorithm with Bregman Distances for Quasiconvex Optimization over the Positive Orthant

Sissy da S. Souza (sissysouzgmail.com)
P. Roberto Oliveira (poliveircos.ufrj.br)
J. X. Cruz Neto (jxavierufpi.br)
A. Soubeyran (soubeyromarin.univ-aix.fr)

Abstract: We present an interior proximal point method with Bregman distance, whose Bregman function is separable and the zone is the interior of the positive orthant, for solving the quasiconvex optimization problem under nonnegative constraints. We establish the well-definedness of the sequence generated by our algorithm and we prove convergence to a solution point when the sequence of parameters tend to zero. When the parameters are bounded above, we get the convergence to a KKT point.

Keywords: proximal methods, interior point algorithms, Bregman distances, quasiconvex programming

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

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Entry Submitted: 11/17/2006
Entry Accepted: 11/17/2006
Entry Last Modified: 07/05/2007

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