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Data-compatibility of algorithms

Yair Censor (yair***at***math.haifa.ac.il)
Maroun Zaknoon (zaknoon***at***arabcol.ac.il)
Alexander J. Zaslavski (ajzasl***at***techunix.technion.ac.il)

Abstract: The data-compatibility approach to constrained optimization, proposed here, strives to a point that is “close enough” to the solution set and whose target function value is “close enough” to the constrained minimum value. These notions can replace analysis of asymptotic convergence to a solution point of infinite sequences generated by specific algorithms. We consider a problem of minimizing a convex function over the intersection of the fixed point sets of nonexpansive mappings and demonstrate the data-compatibility of the Hybrid Subgradient Method (HSM). A string-averaging HSM is obtained as a by-product and relevance to the minimization over disjoint hard and soft constraints sets is discussed.

Keywords: Data-compatiblity, constrained convex minimization, fixed point sets, hybrid method, subgradient, string-averaging, common fixed points, proximity function, nonexpansive operators.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Revised version, October 23, 2020, accepted for publication in: Journal of Applied and Numerical Optimization.

Download: [PDF]

Entry Submitted: 11/26/2019
Entry Accepted: 11/26/2019
Entry Last Modified: 10/23/2020

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