Dual principal component pursuit and orthogonal dictionary learning are two fundamental tools in data analysis, and both of them can be formulated as a manifold optimization problem with nonsmooth objective. algorithm...
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ISBN:
(纸本)9781728143002
Dual principal component pursuit and orthogonal dictionary learning are two fundamental tools in data analysis, and both of them can be formulated as a manifold optimization problem with nonsmooth objective. algorithms with convergence guarantees for solving this kind of problems have been very limited in the literature. In this paper, we propose a novel manifold proximal point algorithm for solving this nonsmooth manifold optimization problem. Numerical results are reported to demonstrate the effectiveness of the proposed algorithm.
A proximal point algorithm with double computational errors for treating zero points of accretive operators is investigated. Strong convergence theorems of zero points are established in a Banach space.
A proximal point algorithm with double computational errors for treating zero points of accretive operators is investigated. Strong convergence theorems of zero points are established in a Banach space.
We obtain existence and convergence theorems for two variants of the proximal point algorithm involving proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.
We obtain existence and convergence theorems for two variants of the proximal point algorithm involving proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.
In this paper, we propose a modified proximal point algorithm for finding a common element of the set of common fixed points of a finite family of quasi-nonexpansive multi-valued mappings and the set of minimizers of ...
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In this paper, we propose a modified proximal point algorithm for finding a common element of the set of common fixed points of a finite family of quasi-nonexpansive multi-valued mappings and the set of minimizers of convex and lower semi-continuous functions. We obtain weak and strong convergence of the proposed algorithm to a common element of the two sets in real Hilbert spaces. A numerical example to support our main results is also given.
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sub...
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In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate from the prospective of variational inequality. Preliminary numerical experiments on testing a sparse minimization problem from signal processing indicate that the proposed algorithm performs better than some well-established methods.
作者：
Moudafi, A.LACO
URA 1586 Université de Limoges Limoges Cedex 87060 France
The proximalalgorithm for saddle-point problems minx ∈X maxy ∈YL(x, y), where X, Y are Hilbert spaces and L: X × Y → R is a proper, closed convex-concave function in X × Y is considered, Under a minimal ...
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In this paper, we propose a new modified proximal point algorithm for a countably infinite family of nonexpansive mappings in complete CAT(0) spaces and prove strong convergence theorems for the proposed process under...
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In this paper, we propose a new modified proximal point algorithm for a countably infinite family of nonexpansive mappings in complete CAT(0) spaces and prove strong convergence theorems for the proposed process under suitable conditions. We also apply our results to solving linear inverse problems and minimization problems. Several numerical examples are given to show the efficiency of the presented method.
We consider the relaxed and contraction-proximal point algorithms in Hilbert spaces. Some conditions on the parameters for guaranteeing the convergence of the algorithm are relaxed or removed. As a result, we extend s...
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We consider the relaxed and contraction-proximal point algorithms in Hilbert spaces. Some conditions on the parameters for guaranteeing the convergence of the algorithm are relaxed or removed. As a result, we extend some recent results of Ceng-Wu-Yao and Noor-Yao.
Recently, Gregorio and Oliveira developed a proximalpoint scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadrat...
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Recently, Gregorio and Oliveira developed a proximalpoint scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al, as regularization. In this study, a variation of this method is proposed, using the regularization with logarithm and quasi-distance. By restricting it to a certain class of quasi-distances that are Lipschitz continuous and coercive in any of their arguments, we show that any sequence { (x(k), z(k)) subset of R-n x R-m generated by the method satisfies: {z(k)} is convergent: and {x(k)} is bounded and its accumulation points are weak Pareto solutions of the unconstrained multi-objective optimization problem (C) 2015 Elsevier Inc. All rights reserved.
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