Eliahu Levy – Optimization Online

Limits of eventual families of sets with application to algorithms for the common fixed point problem

Published: 2022/03/08

Convex Optimization, Nonlinear Optimization common fixed points, cutters, eventual families, firmly nonexpansive operators, Hausdorff topological space, multifamily, multiset, set convergence

We present an abstract framework for asymptotic analysis of convergence based on the notions of eventual families of sets that we define. A family of subsets of a given set is called here an “eventual family” if it is upper hereditary with respect to inclusion. We define accumulation points of eventual families in a Hausdorff … Read more

An analysis of the superiorization method via the principle of concentration of measure

Published: 2019/09/28

Yair Censor

Eliahu Levy

Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Nonlinear Optimization concentration of measure, feasibility-seeking algorithm, hilbert-schmidt norm, linear superiorization, perturbation resilience, random matrix, superiorization, superiorization matrix, target function reduction

The superiorization methodology is intended to work with input data of constrained minimization problems, i.e., a target function and a constraints set. However, it is based on an antipodal way of thinking to the thinking that leads constrained minimization methods. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce … Read more