کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607498 1337862 2012 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Attouch–Théra duality revisited: Paramonotonicity and operator splitting
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Attouch–Théra duality revisited: Paramonotonicity and operator splitting
چکیده انگلیسی

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 [H.H. Bauschke, P.L. Combettes, D.R. Luke, A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space, Journal of Approximation Theory 141 (2006) 63–69] from normal cone operators to paramonotone operators. Our results are illustrated through numerous examples.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 164, Issue 8, August 2012, Pages 1065–1084
نویسندگان
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