On Dual Convergence and the Rate of Primal Convergence of Bregman’s Convex Programming Method

Abstract

Bregman’s method is an iterative algorithm for solving optimization problems with convex objective and linear inequality constraints. It generates two sequences: one, the primal one, is known to converge to the solution of the problem. Under the assumption of smoothness of the objective function at the solution, it is proved that the other sequence, the dual one, converges to a solution of the dual problem, and that the rate of convergence of the primal sequence is at least linear.