In this paper, we modify the proximal point algorithm for finding common fixed points in CAT(0) spaces for nonlinear multivalued mappings and a minimizer of a convex function and prove Delta-convergence of the propose...
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In this paper, we modify the proximal point algorithm for finding common fixed points in CAT(0) spaces for nonlinear multivalued mappings and a minimizer of a convex function and prove Delta-convergence of the proposed algorithm. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.
The purpose of this article is twofold. One is to establish a proximal point algorithm for finding a minimizer of a proper convex and lower semi-continuous function and fixed points of quasi-pseudo-contractive mapping...
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The purpose of this article is twofold. One is to establish a proximal point algorithm for finding a minimizer of a proper convex and lower semi-continuous function and fixed points of quasi-pseudo-contractive mappings in CAT(0) spaces. The other is to point out and correct a basic and conceptual error in a paper of Ugwunnadi et al. [Theorem 3.1, J. Fixed point Theory Appl. (2018) 20: 82].
In this paper, we propose an asymmetric proximal point algorithm for solving variational inequality problems. The algorithm is asymmetric in the sense that the matrix in the linear proximal term is not necessary to be...
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In this paper, we propose an asymmetric proximal point algorithm for solving variational inequality problems. The algorithm is asymmetric in the sense that the matrix in the linear proximal term is not necessary to be a symmetric matrix, which makes the method more flexible, especially in dealing with problems with separable structures. Under some suitable conditions, we prove the global linear convergence of the algorithm. To make the method more practical, we allow the subproblem to be solved in an approximate manner and a flexible inaccuracy criterion with constant parameter is adopted. Finally, we report some preliminary numerical results.
作者：
Gregorio, R. M.Oliveira, P. R.Alves, C. D. S.Univ Fed Rural Rio de Janeiro
Inst Multidisciplinar Dept Tecnol & Linguagens Inst Ciencias ExatasPrograma Posgrad Modelgem Ma Ave Governador Roberto da Silveira S-NBloco Adm BR-2602074 Nova Iguacu RJ Brazil Univ Fed Rio de Janeiro
Inst Alberto Luiz Coimbra Posgrad & Pesquisa Engn Programa Engn Sistemas & Comp Ctr Tecnol Ave Horacio Macedo 2030Bloco HSala 319 BR-21941914 Rio De Janeiro RJ Brazil
This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric positive semidefinite matrices, and extends it to domains...
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This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric positive semidefinite matrices, and extends it to domains of positivity of reducible type, in a nonlinear sense and in a Riemannian setting. Several computational experiments with weighted L-P (p = 1, 2) centers of mass are performed to demonstrate the practical feasibility of the method. (C) 2018 Elsevier Inc. All rights reserved.
In the literature, there are a few researches to design some parameters in the proximal point algorithm (PPA), especially for the multi-objective convex optimizations. Introducing some parameters to PPA can make it mo...
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In the literature, there are a few researches to design some parameters in the proximal point algorithm (PPA), especially for the multi-objective convex optimizations. Introducing some parameters to PPA can make it more flexible and attractive. Mainly motivated by our recent work [Bai et al. A parameterized proximal point algorithm for separable convex optimization. Optim Lett. (2017) doi: 10.1007/s11590-017-1195-9], in this paper we develop a general parameterized PPA with a relaxation step for solving the multi-block separable structured convex programming. By making use of the variational inequality and some mathematical identities, the global convergence and the worst-case caseO(1/t) convergence rate of the proposed algorithm are established. Preliminary numerical experiments on solving a sparse matrix minimization problem from statistical learning validate that our algorithm is more efficient than several state-of-the-art algorithms.
This note is a reaction to the recent paper by Rouhani and Moradi (J Optim Theory Appl 172:222-235, 2017), where a proximal point algorithm proposed by Boikanyo and Moroanu (Optim Lett 7:415-420, 2013) is discussed. N...
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This note is a reaction to the recent paper by Rouhani and Moradi (J Optim Theory Appl 172:222-235, 2017), where a proximal point algorithm proposed by Boikanyo and Moroanu (Optim Lett 7:415-420, 2013) is discussed. Noticing the inappropriate formulation of that algorithm, we propose a more general algorithm for approximating zeros of a maximal monotone operator on a Hilbert space. Besides the main result on the strong convergence of the sequences generated by this new algorithm, we discuss some particular cases, including the approximation of minimizers of convex functionals and present two examples to illustrate the applicability of the algorithm. The note clarifies and extends both the papers quoted above.
We show that Dykstra's splitting for projecting onto the intersection of convex sets can be extended to minimize the sum of convex functions and a regularizing quadratic function. We give conditions for which conv...
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We show that Dykstra's splitting for projecting onto the intersection of convex sets can be extended to minimize the sum of convex functions and a regularizing quadratic function. We give conditions for which convergence to the primal minimizer holds so that more than one convex function can be minimized at a time, the convex functions are not necessarily sampled in a cyclic manner, and the SHQP strategy for problems involving the intersection of more than one convex set can be applied. When the sum does not involve the regularizing quadratic function, we discuss an approximate proximalpoint method combined with Dykstra's splitting to minimize this sum.
In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove -convergence of the generated sequence to a critical point (which is define...
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In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove -convergence of the generated sequence to a critical point (which is defined in the text) of an objective quasi-convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces.
In this paper, we prove the Δ-convergence of a modified proximal point algorithm for common fixed points in a CAT(0) space for different classes of generalized nonexpansive mappings including a total asymptotically n...
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In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to b...
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In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case O(1/t) convergence rate, where t denotes the iteration number. By properly choosing the algorithm parameters, numerical experiments on solving a sparse optimization problem arising from statistical learning show that our P-PPA could perform significantly better than other state-of-the-art methods, such as the alternating direction method of multipliers and the relaxed proximal point algorithm.
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