2019/08/20 by Andrzej Cegielski, Cegielski, Andrzej, Aviv Gibali +5
Computer Science · Mathematics · #47H09 #47H10 #47J20 #47J25 #65K15 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC #msc:47H09 #msc:47H10 #msc:47J20 #msc:47J25 #msc:65K15
paper · pdf · doi:10.48550/arxiv.1908.07398
arxiv created 2019/08/20 · openalex publication_date 2019/08/20 · arxiv updated 2019/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study variational inequalities which are governed by a strongly monotone and Lipschitz continuous operator F over a closed and convex set S. We assume that S=C∩ A-1(Q) is the nonempty solution set of a (multiple-set) split convex feasibility problem, where C and Q are both closed and convex subsets of two real Hilbert spaces \mathcal H1 and \mathcal H2, respectively, and the operator A acting between them is linear. We consider a modification of the gradient projection method the main idea of which is to replace at each step the metric projection onto S by another metric projection onto a half-space which contains S. We propose three variants of a method for constructing the above-mentioned half-spaces by employing the multiple-set and the split structure of the set S. For the split part we make use of the Landweber transform.