2017/12/01 by Heinz H. Bauschke, Bauschke, Heinz H., Walaa M. Moursi +1
Computer Science · Immunology and Microbiology · Mathematics · #47H09 Secondary 47H10 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Phagocytosis and Immune Regulation #Primar 47H05
paper · pdf · doi:10.48550/arxiv.1712.00487
openalex publication_date 2017/12/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Maximally monotone operators and firmly nonexpansive mappings play key roles\nin modern optimization and nonlinear analysis. Five years ago, it was shown\nthat if finitely many firmly nonexpansive operators are all asymptotically\nregular (i.e., the have or "almost have" fixed points), then the same is true\nfor compositions and convex combinations. In this paper, we derive bounds on\nthe magnitude of the minimal displacement vectors of compositions and of convex\ncombinations in terms of the displacement vectors of the underlying operators.\nOur results completely generalize earlier works. Moreover, we present various\nexamples illustrating that our bounds are sharp.\n