Stability of a convex feasibility problem

Carlo Alberto Bernardi (), Enrico Miglierina () and Elena Molho ()
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Carlo Alberto Bernardi: Università Cattolica del Sacro Cuore
Enrico Miglierina: Università Cattolica del Sacro Cuore
Elena Molho: Università degli Studi di Pavia

Journal of Global Optimization, 2019, vol. 75, issue 4, No 7, 1077 pages

Abstract: Abstract The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets A and B in a normed space X. More generally, we can consider the problem of finding (if possible) two points in A and B, respectively, which minimize the distance between the sets. In the present paper, we study some stability properties for the convex feasibility problem: we consider two sequences of sets, each of them converging, with respect to a suitable notion of set convergence, respectively, to A and B. Under appropriate assumptions on the original problem, we ensure that the solutions of the perturbed problems converge to a solution of the original problem. We consider both the finite-dimensional and the infinite-dimensional case. Moreover, we provide several examples that point out the role of our assumptions in the obtained results.

Keywords: Convex feasibility problem; Stability; Set-convergence; Primary 90C25; Secondary 90C31; 49J53 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-019-00806-w

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