averaged nonexpansive operator – Optimization Online

Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems

Published: 2023/03/07

Global Optimization Theory, Stochastic Approaches, Stochastic Programming averaged nonexpansive operator, markov chain, stochastic convex feasibility

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant mea- sure the stochastic fixed point problem. This generalizes earlier work studying the stochastic feasibility problem, namely, to find points that are, with probability 1, fixed points of … Read more

Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping

Published: 2014/04/29, Updated: 2014/05/27

Patrick L. Combettes

Jean-Christophe Pesquet

Convex Optimization, Nonsmooth Optimization, Stochastic Programming averaged nonexpansive operator, block-coordinate algorithm, douglas-rachford algorithm, fixed point algorithm, forward-backward algorithm, primal-dual operator splitting, stochastic quasi fejér sequence, structured minimization problem

This work investigates the properties of stochastic quasi-Fejér monotone sequences in Hilbert spaces and emphasizes their pertinence in the study of the convergence of block-coordinate fixed point methods. The iterative methods under investigation feature random sweeping rules to select the blocks of variables that are activated over the course of the iterations and allow for … Read more