Feasibility problems via paramonotone operators in a convex setting

J. Parra López, J. Camacho Moro, M. J. Cánovas Cánovas, J. E. Martínez Legaz

This talk is focused on some properties of paramonotone operators and their application to certain feasibility problems for convex sets and systems in the Euclidean space. In particular, we show that operators that are simultaneously paramonotone and bimonotone are constant on their domains, and this fact is applied to tackle two particular situations. The first one, closely related to simultaneous projections, deals with a finite amount of convex sets with an empty intersection and tackles the problem of finding the smallest perturbations (in the sense of translations) of these sets to reach a nonempty intersection. The second is focused on the distance to feasibility; specifically, given an inconsistent convex inequality system, our goal is to compute/estimate the smallest right-hand side perturbations that reach feasibility. We advance that this work derives lower and upper estimates of such a distance, which become the exact value when confined to linear systems.

Keywords: Distance function, convex inequalities, distance to feasibility, paramonotone operators, displacement mapping

GT13.OPTCONT3 Invited Session
November 7, 2023  3:30 PM
HC2: Canónigos Room 2

M. J. Cánovas Cánovas, J. Camacho Moro, H. Gfrerer, J. Parra López

H. Gfrerer, J. Outrata

J. Rückmann, D. Hernández Escobar