Dual convergence of the proximal point method with Bregman distances for linear programming

Authors:
J. X. Cruz Neto;O. P. Ferreira;A. N. Iusem;R. D. C. Monteiro
Affiliations:
DM, Universidade Federal do Piauí, Teresina, tPI, Brazil;IME, Universidade Federal de Goiás, Goiânia, tGO, Brazil;IMPA, Estrada Dona Castorina 110, Rio de Janeiro, tRJ, Brazil;School of ISyE, Georgia Tech, Atlanta, tGeorgia, USA
Venue:
Optimization Methods & Software
Year:
2007

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Abstract

In this article, we consider the proximal point method with Bregman distance applied to linear programming problems, and study the dual sequence obtained from the optimal multipliers of the linear constraints of each subproblem. We establish the convergence of this dual sequence, as well as convergence rate results for the primal sequence, for a suitable family of Bregman distances. These results are obtained by studying first the limiting behavior of a certain perturbed dual path and then the behavior of the dual and primal paths.