averaged projections – Optimization Online

Global convergence and acceleration of fixed point iterations of union upper semicontinuous operators: proximal algorithms, alternating and averaged nonconvex projections, and linear complementarity problems

Published: 2022/02/21, Updated: 2022/07/19

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 propose a unified framework to analyze fixed point iterations of a set-valued operator that is the union of a finite number of upper semicontinuous maps, each with a nonempty closed domain and compact values. We discuss global convergence, local linear convergence under a calmness condition, and component identification, and further propose acceleration strategies that … 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