2011/10/21 by Heinz H. Bauschke, Bauschke, Heinz H., Radu I. Bot +7 · 1 citation
Computer Science · Mathematics · #41A50 #47H05 #47H09 #47N10 #49M27 #49N15 #65K05 #65K10 #90C25 (Primary) 47J05 #90C46 (Secondary) #Advanced Optimization Algorithms Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.FA #math.OC #msc:41A50 #msc:47H05 #msc:47H09 #msc:47J05 #msc:47N10 #msc:49M27 #msc:49N15 #msc:65K05 #msc:65K10 #msc:90C25 #msc:90C46
paper · pdf · doi:10.48550/arxiv.1110.4877
arxiv created 2011/10/21 · openalex publication_date 2011/10/21 · arxiv updated 2011/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of finding the zeros of the sum of two maximally monotone operators is of fundamental importance in optimization and variational analysis. In this paper, we systematically study Attouch-Théra duality for this problem. We provide new results related to Passty's parallel sum, to Eckstein and Svaiter's extended solution set, and to Combettes' fixed point description of the set of primal solutions. Furthermore, paramonotonicity is revealed to be a key property because it allows for the recovery of all primal solutions given just one arbitrary dual solution. As an application, we generalize the best approximation results by Bauschke, Combettes and Luke [J. Approx. Theory 141 (2006), 63-69] from normal cone operators to paramonotone operators. Our results are illustrated through numerous examples.