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

Renato Monteiro | Cruz Neto, João Xavier | Ferreira, Orizon Pereira | Iusem, Alfredo Noel

Keywords: proximal point method | brrier function | Bregman distance | convergence rate

In this paper we consider the proximal point method with Bregman distances applied to linear programming problems, and study the dual sequence obtained from the optimal multipliers of the lienar constraints of each subproblem. We establish the convergence of this dual sequence, as well of convergenmce 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 path.

Anexos:

• iusmon2n.ps