Data-compatibility of algorithms for constrained convex optimization

Prof. Yair Censor, Dr. Maroun Zaknoon, Prof. Alexander J. Zaslavski

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 non-expansive mappings and demonstrate the data-compatibility of the Hybrid Sub-gradient 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.