On Dual Convergence of the Generalized Proximal Point Method with Bregman Distances

Authors:
Alfredo Iusem;Renato D.C. Monteiro
Affiliations:
-;-
Venue:
Mathematics of Operations Research
Year:
2000

Citing 0
Cited 3

Some recent advances in projection-type methods for variational inequalities

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Dual convergence of the proximal point method with Bregman distances for linear programming

Optimization Methods & Software
On the convergence of the entropy-exponential penalty trajectories and generalized proximal point methods in semidefinite optimization

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

The use of generalized distances (e.g., Bregman distances), instead of the Euclidean one, in the proximal point method for convex optimization, allows for elimination of the inequality constraints from the subproblems. In this paper we consider the proximal point method with Bregman distances applied to linearly constrained convex optimization problems, and study the behavior of the dual sequence obtained from the optimal multipliers of the linear constraints of each subproblem. Under rather general assumptions, which cover most Bregman distances of interest, we obtain an ergodic convergence result, namely that a sequence of weighted averages of the dual sequence converges to a specific point of the dual optimal set. As an intermediate result, we prove under the same assumptions that the dual central path generated by a large class of barriers, including the generalized Bregman distances, converges to the same point.