Solving Proximal Split Feasibility Problems without prior knowledge of operator norms

A. Moudafi () and B.S. Thakur ()
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A. Moudafi: CEREGMIA, Université des Antilles et de la Guyane
B.S. Thakur: School of Studies in Mathematics, Pt.Ravishankar Shukla University, Raipur, 492010, India

No 2013-08, Documents de Travail from CEREGMIA, Université des Antilles et de la Guyane

Abstract: In this paper our interest is in investigating properties and numerical solutions of Proximal Split feasibility Problems. First, we consider the problem of nding a point which minimizes a convex function f such that its image under a bounded linear op- erator A minimizes another convex function g. Based on an idea introduced in [9], we propose a split proximal algorithm with a way of selecting the step-sizes such that its implementation does not need any prior information about the operator norm. Because the calculation or at least an estimate of the operator norm kAk is not an easy task. Secondly, we investigate the case where one of the two involved functions is prox-regular, the novelty of this approach is that the associated proximal mapping is not nonexpan- sive any longer. Such situation is encountered, for instance, in numerical solution to phase retrieval problem in crystallography, astronomy and inverse scattering [10] and is therefore of great practical interest.

Pages: 10 pages
Date: 2013-04
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