2017/09/17 by Yair Censor, Censor, Yair, Rafiq Mansour +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1709.05627
openalex publication_date 2017/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Convex feasibility problems require to find a point in the intersection of a\nfinite family of convex sets. We propose to solve such problems by performing\nset-enlargements and applying a new kind of projection operators called valiant\nprojectors. A valiant projector onto a convex set implements a special\nrelaxation strategy, proposed by Goffin in 1971, that dictates the move toward\nthe projection according to the distance from the set. Contrary to past\nrealizations of this strategy, our valiant projection operator implements the\nstrategy in a continuous fashion. We study properties of valiant projectors and\nprove convergence of our new valiant projections method. These results include\nas a special case and extend the 1985 automatic relaxation method of Censor.\n