total convexity – Optimization Online

A Stochastic Bregman Primal-Dual Splitting Algorithm for Composite Optimization

Published: 2021/12/22

We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in the computation of gradient terms within the algorithm. We show ergodic convergence in expectation of the Lagrangian optimality gap with a … Read more

Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces

Published: 2005/01/16, Updated: 2005/01/18

Dan Butnariu

Elena Resmerita

Convex and Nonsmooth Optimization bregman distance, bregman projection, e-space, essential strict convexity, inverse monotone operator, inverse strongly-monotone operator, mosco convergence, relative projection, total convexity, uniform convexity

The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity … Read more