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pro vyhledávání: '"Walaa M. Moursi"'
Autor:
Pontus Giselsson, Walaa M. Moursi
Publikováno v:
Fixed Point Theory and Algorithms for Sciences and Engineering, Vol 2021, Iss 1, Pp 1-38 (2021)
Abstract Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particu
Externí odkaz:
https://doaj.org/article/dbb8662ac93844f39aa2afcd9c5fd7c3
Autor:
Heinz H. Bauschke, Walaa M. Moursi
Publikováno v:
Mathematics of Operations Research.
More than 40 years ago, Lions and Mercier introduced in a seminal paper the Douglas–Rachford algorithm. Today, this method is well-recognized as a classic and highly successful splitting method to find minimizers of the sum of two (not necessarily
Publikováno v:
The American Mathematical Monthly. 128:796-809
In 1964, Michael Edelstein presented an amazing affine isometry acting on the space of square-summable sequences. This operator has no fixed points, but a suborbit that converges to 0 while another...
Publikováno v:
Mathematical Programming. 189:55-74
The correspondence between the monotonicity of a (possibly) set-valued operator and the firm nonexpansiveness of its resolvent is a key ingredient in the convergence analysis of many optimization algorithms. Firmly nonexpansive operators form a prope
Autor:
Walaa M. Moursi, Heinz H. Bauschke
Publikováno v:
SIAM Journal on Optimization. 30:2559-2576
The Douglas-Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one minimizer. In the
Publikováno v:
Computational Optimization and Applications. 74:627-643
Many numerical methods for conic problems use the homogenous primal–dual embedding, which yields a primal–dual solution or a certificate establishing primal or dual infeasibility. Following Themelis and Patrinos (IEEE Trans Autom Control, 2019),
Autor:
Lieven Vandenberghe, Walaa M. Moursi
Publikováno v:
Journal of Optimization Theory and Applications. 183:179-198
The Douglas–Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper, closed, and convex functions and, more generally, two maximally monotone operators. Recent results concerned with
Autor:
Walaa M. Moursi, Heinz H. Bauschke
Publikováno v:
Optimization Letters. 12:1465-1474
Maximally monotone operators and firmly nonexpansive mappings play key roles in modern optimization and nonlinear analysis. Five years ago, it was shown that if finitely many firmly nonexpansive operators are all asymptotically regular (i.e., they ha
Autor:
Walaa M. Moursi
Publikováno v:
Journal of Optimization Theory and Applications. 176:605-624
The forward–backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a n
Publikováno v:
Operations Research Letters. 46:585-587
Aragon Artacho and Campoy recently proposed a new method for computing the projection onto the intersection of two closed convex sets in Hilbert space; moreover, they proposed in 2018 a generalization from normal cone operators to maximally monotone