Minimum L1-distance projection onto the boundary of a convex set: Simple characterization

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113931We show that the minimum distance projection in the L1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a polyhedron leads to either an elementary minmax problem or a set of easily solved linear programs, depending upon whether the polyhedron is given as the intersection of a set of half spaces or as the convex hull of a set of extreme points. The outcome is an easier and more straightforward derivation of the special case results given in a recent paper by Briec.5 pagesOptimization and Control90C25Minimum L1-distance projection onto the boundary of a convex set: Simple characterizationtext