variable strings – Optimization Online

String-Averaging Projected Subgradient Methods for Constrained Minimization

Published: 2013/08/29

Constrained Nonlinear Optimization, Convex Optimization fixed point, hilbert space, metric projection, nonexpansive operator, perturbation resilience, projected subgradient minimization, string-averaging projection methods, superiorization method, variable strings, variable weights

We consider constrained minimization problems and propose to replace the projection onto the entire feasible region, required in the Projected Subgradient Method (PSM), by projections onto the individual sets whose intersection forms the entire feasible region. Specifically, we propose to perform such projections onto the individual sets in an algorithmic regime of a feasibility-seeking iterative … Read more

Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods

Published: 2012/06/01

Yair Censor

Alexander J. Zaslavski

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