averaged projections – Optimization Online

Global convergence and acceleration of projection methods for feasibility problems involving union convex sets

Published: 2022/02/21, Updated: 2023/07/14

Complementarity and Variational Inequalities, Nonlinear Optimization, Nonsmooth Optimization alternating projections, averaged projections, fixed point algorithm, global convergence, Linear complementarity problem, nonconvex optimization, proximal methods

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for analyzing global convergence by means of studying fixed-point iterations of a set-valued operator that is the union of … Read more

Local convergence for alternating and averaged nonconvex projections

Published: 2007/09/01

Adrian Lewis

Jérôme Malick

Russell Luke

Constrained Nonlinear Optimization, Control Applications, Nonsmooth Optimization alternating projection methods, averaged projections, distance to ill-posedness, extremal principle, linear convergence, metric regularity, nonconvex, prox-regularity, variational analysis

The idea of a finite collection of closed sets having “strongly regular intersection” at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically, we consider the case of two sets, one of which we assume to be suitably “regular” (special cases being convex … Read more