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.

De Bernardi, C. A., Miglierina, E., Molho, E., Stability of a convex feasibility problem, <<JOURNAL OF GLOBAL OPTIMIZATION>>, 2019; 75 (4): 1061-1077. [doi:10.1007/s10898-019-00806-w] [http://hdl.handle.net/10807/142369]

Stability of a convex feasibility problem

De Bernardi, Carlo Alberto
;
Miglierina, Enrico
;
2019

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.
2019
Inglese
De Bernardi, C. A., Miglierina, E., Molho, E., Stability of a convex feasibility problem, <<JOURNAL OF GLOBAL OPTIMIZATION>>, 2019; 75 (4): 1061-1077. [doi:10.1007/s10898-019-00806-w] [http://hdl.handle.net/10807/142369]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/142369
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