共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, we study some non-traditional schemes of proximal point algorithm for nonsmooth convex functionals in a Banach space. The proximal approximations to their minimal points and/or their minimal values are considered separately for unconstrained and constrained minimization problems on convex closed sets. For the latter we use proximal point algorithms with the metric projection operators and first establish the estimates of the convergence rate with respect to functionals. We also investigate the perturbed projection proximal point algorithms and prove their stability. Some results concerning the classical proximal point method for minimization problems in a Banach space is also presented in this paper. 相似文献
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We analyze the behavior of a parallel proximal point method for solving convex optimization problems in reflexive Banach spaces. Similar algorithms were known to converge under the implicit assumption that the norm of the space is Hilbertian. We extend the area of applicability of the proximal point method to solving convex optimization problems in Banach spaces on which totally convex functions can be found. This includes the class of all smooth uniformly convex Banach spaces. Also, our convergence results leave more flexibility for the choice of the penalty function involved in the algorithm and, in this way, allow simplification of the computational procedure. 相似文献
4.
提出了一类修正的近似点算法并讨论了算法的收敛性质及其Budle变形的收敛性质。 相似文献
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The aim of this paper is to study the convergence of two proximal algorithms via the notion of (α, r)-relaxed cocoercivity without Lipschitzian continuity. We will show that this notion is enough to obtain some interesting convergence theorems without any Lipschitz-continuity assumption. The relaxed cocoercivity case is also investigated. 相似文献
6.
BinayakS.Choudhury 《分析论及其应用》2003,19(2):99-107
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extersion of a known theorem in the corresponding non-random case. 相似文献
7.
The subject of this paper is the inexact proximal point algorithm of usual and Halpern type in non-positive curvature metric spaces. We study the convergence of the sequences given by the inexact proximal point algorithm with non-summable errors. We also prove the strong convergence of the Halpern proximal point algorithm to a minimum point of the convex function. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces. 相似文献
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Huang Jianfeng Wang Yuanheng 《高校应用数学学报(英文版)》2007,22(3):311-315
This paper studies the convergence of the sequence defined by x0∈C,xn 1=αnu (1-αn)Txn,n=0,1,2,…, where 0 ≤αn ≤ 1, limn→∞αn = 0, ∑∞n=0 αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results. 相似文献
9.
《Optimization》2012,61(5):955-980
ABSTRACTIn this work, we suggest modifications of the self-adaptive method for solving the split feasibility problem and the fixed point problem of nonexpansive mappings in the framework of Banach spaces. Without the assumption on the norm of the operator, we prove that the sequences generated by our algorithms weakly and strongly converge to a solution of the problems. The numerical experiments are demonstrated to show the efficiency and the implementation of our algorithms. 相似文献
10.
In this paper, we introduce an iterative sequence for finding a solution of a maximal monotone operator in a uniformly convex Banach space. Then we first prove a strong convergence theorem, using the notion of generalized projection. Assuming that the duality mapping is weakly sequentially continuous, we next prove a weak convergence theorem, which extends the previous results of Rockafellar [SIAM J. Control Optim.
14 (1976), 877–898] and Kamimura and Takahashi [J. Approx. Theory
106 (2000), 226–240]. Finally, we apply our convergence theorem to the convex minimization problem and the variational inequality problem. 相似文献
11.
In this paper, we introduce a new W-mapping and present an iterative algorithm for an infinite family of strict pseudo-contractions. Strong convergence theorems are proved in Banach spaces. Our results improve and extend the corresponding result announced by Cai and Hu [G. Cai, C. Hu, Strong convergence theorems of modified Ishikawa iterative process with errors for an infinite family of strict pseudo-contractions, Nonlinear Anal. 71(12) (2009) 6044-6053]. 相似文献
12.
Habtu Zegeye 《Journal of Mathematical Analysis and Applications》2008,343(2):663-671
Let E be a uniformly convex and 2-uniformly smooth real Banach space with dual E∗. Let be a Lipschitz continuous monotone mapping with A−1(0)≠∅. For given u,x1∈E, let {xn} be generated by the algorithm xn+1:=βnu+(1−βn)(xn−αnAJxn), n?1, where J is the normalized duality mapping from E into E∗ and {λn} and {θn} are real sequences in (0,1) satisfying certain conditions. Then it is proved that, under some mild conditions, {xn} converges strongly to x∗∈E where Jx∗∈A−1(0). Finally, we apply our convergence theorems to the convex minimization problems. 相似文献
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In this paper, we analyse the convergence rate of the sequence of objective function values of a primal-dual proximal-point algorithm recently introduced in the literature for solving a primal convex optimization problem having as objective the sum of linearly composed infimal convolutions, nonsmooth and smooth convex functions and its Fenchel-type dual one. The theoretical part is illustrated by numerical experiments in image processing. 相似文献
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Viscosity iterative algorithm for variational inequality problems and fixed point problems of strict pseudo-contractions in uniformly smooth Banach spaces 下载免费PDF全文
Gang Cai 《数学学报(英文版)》2015,31(9):1435-1448
The purpose of this paper is to study a new viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for finite inversely strongly accretive mappings and the set of common fixed points for a countable family of strict pseudo-contractions in uniformly smooth Banach spaces. We prove some strong convergence theorems under some suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others in the literature. 相似文献
15.
We prove strong convergence theorems for multimaps under mild conditions, which include Browder's convergence theorem as well as Reich's convergence theorem. We thus provide a partial answer to Jung's question.
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In this note, a small gap is corrected in the proof of H.K. Xu [Theorem 3.3, A regularization method for the proximal point
algorithm, J. Glob. Optim. 36, 115–125 (2006)], and some strict restriction is removed also.
相似文献
17.
W.M. Kozlowski 《Journal of Mathematical Analysis and Applications》2011,377(1):43-52
Let X be a uniformly convex Banach space with the Opial property. Let T:C→C be an asymptotic pointwise nonexpansive mapping, where C is bounded, closed and convex subset of X. In this paper, we prove that the generalized Mann and Ishikawa processes converge weakly to a fixed point of T. In addition, we prove that for compact asymptotic pointwise nonexpansive mappings acting in uniformly convex Banach spaces, both processes converge strongly to a fixed point. 相似文献
18.
H. H. Bauschke J. V. Burke F. R. Deutsch H. S. Hundal J. D. Vanderwerff 《Proceedings of the American Mathematical Society》2005,133(6):1829-1835
In 1991, Güler constructed a proximal point iteration that converges weakly but not in norm. By building on a recent result of Hundal, we present a new, considerably simpler, example of this type.
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Parin Chaipunya 《Optimization》2017,66(10):1647-1665
Proximal point method is one of the most influential procedure in solving nonlinear variational problems. It has recently been introduced in Hadamard spaces for solving convex optimization, and later for variational inequalities. In this paper, we study the general proximal point method for finding a zero point of a maximal monotone set-valued vector field defined on a Hadamard space and valued in its dual. We also give the relation between the maximality and Minty’s surjectivity condition, which is essential for the proximal point method to be well-defined. By exploring the properties of monotonicity and the surjectivity condition, we were able to show under mild assumptions that the proximal point method converges weakly to a zero point. Additionally, by taking into account the metric subregularity, we obtained the local strong convergence in linear and super-linear rates. 相似文献
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In this paper, we first characterize finite convergence of an arbitrary iterative algorithm for solving the variational inequality problem (VIP), where the finite convergence means that the algorithm can find an exact solution of the problem in a finite number of iterations. By using this result, we obtain that the well-known proximal point algorithm possesses finite convergence if the solution set of VIP is weakly sharp. As an extension, we show finite convergence of the inertial proximal method for solving the general variational inequality problem under the condition of weak g-sharpness. 相似文献