2018/06/26 by De Bernardi, Carlo Alberto, Miglierina, Enrico, Molho, Elena · 1 citation
#49j53 #90c25 #90c31 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1806.10033
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.