Data-compatible solutions of constrained convex optimization
Abstract: The data-compatibility approach to constrained convex 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 define and study data-compatibility with the data of a constrained minimization problem in a Hilbert space and demonstrate it on a problem of minimizing a convex function over the intersection of the fixed point sets of nonexpansive mappings. An iterative algorithm, which we call the Hybrid Subgradient Method (HSM), is proposed and investigated with regard to its ability to generate data-compatible points for the problem at hand. A string-averaging HSM is obtained as a by-product.
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: Preprint, November 2019.
Entry Submitted: 11/26/2019
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