nonexpansive operator – Page 2 – Optimization Online

Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods

Published: 2012/06/01

Biomedical Applications, Convex Optimization, Parallel Algorithms dynamic string-averaging, fixed point, hilbert space, metric projection, nonexpansive operator, perturbation resilience, projection methods, superiorization method, variable strings, variable weights

We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the … Read more

A von Neumann Alternating Method for Finding Common Solutions to Variational Inequalities

Published: 2012/02/03

Yair Censor

Aviv Gibali

Simeon Reich

Complementarity and Variational Inequalities, Nonlinear Optimization alternating method, averaged operator, fixed point, hilbert space, inverse strongly-monotone operator, metric projection, nonexpansive operator, resolvent, variational inequality

Modifying von Neumann’s alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space. Citation Nonlinear Analysis Series A: Theory, Methods & … Read more