We investigate the condition of coefficients for a generalized proximal point algorithm in uniformly convex Banach spaces. Using the information of the current point to determine the coefficient for the next point, we...
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We investigate the condition of coefficients for a generalized proximal point algorithm in uniformly convex Banach spaces. Using the information of the current point to determine the coefficient for the next point, we obtain weak convergence of the iterative scheme to a common zero of a sequence of m-accretive operators under a weaker assumption. (C) 2009 Elsevier Ltd. All rights reserved.
K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonex-pansive mappings, nonexpansive semigroups, and proximal point algorithm for zero point of monotone operators in Hilbert spaces by usi...
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K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonex-pansive mappings, nonexpansive semigroups, and proximal point algorithm for zero point of monotone operators in Hilbert spaces by using the hybrid method in mathematical programming. The purpose of this paper is to modify the hybrid iteration method of K. Nakajo and W. Takahashi through the monotone hybrid method, and to prove strong convergence theorems. The convergence rate of iteration process of the monotone hybrid method is faster than that of the iteration process of the hybrid method of K. Nakajo and W. Takahashi. In the proofs in this article, Cauchy sequence method is used to avoid the use of the demiclosedness principle and Opial＇s condition.
Nakajo and Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379] proved strong convergence theorems for nonexpa...
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Nakajo and Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379] proved strong convergence theorems for nonexpansive mappings, nonexpansive semigroups and the proximal point algorithm for zero-point of monotone operators in Hilbert spaces by the CQ iteration method. The purpose of this paper is to modify the CQ iteration method of K. Nakajo and W. Takahashi using the monotone CQ method, and to prove strong convergence theorems. In the proof process of this article, the Cauchy sequence method is used, so we proceed without use of the demiclosedness principle and Opial's condition, and other weak topological techniques. (C) 2007 Elsevier Ltd. All rights reserved.
作者：
Li, MinSE Univ
Dept Management Sci & Engn Sch Econ & Management Nanjing 210096 Peoples R China
In this work, the conditions on the well-known Bregman function in generalized approximate proximal point algorithms (APPA) are replaced by some easily checked ones, which are more practical. The resulting new general...
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In this work, the conditions on the well-known Bregman function in generalized approximate proximal point algorithms (APPA) are replaced by some easily checked ones, which are more practical. The resulting new generalized APPA with optimal step sizes converges to a solution globally under rather relaxed restrictions on the error sequence. (C) 2007 Elsevier Ltd. All rights reserved.
To solve monotone variational inequalities, some existing APPA-based descent methods utilize the iterates generated by the well-known approximate proximal point algorithms (APPA) to construct descent directions. This ...
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To solve monotone variational inequalities, some existing APPA-based descent methods utilize the iterates generated by the well-known approximate proximal point algorithms (APPA) to construct descent directions. This paper aims at improving these APPA-based descent methods by incorporating optimal step-sizes in both the extra-gradient steps and the descent steps. Global convergence is proved under mild assumptions. The superiority to existing methods is verified both theoretically and computationally. (C) 2007 Elsevier B.V. All rights reserved.
A class of nonlinear operators in Banach spaces is proposed. We call each operator in this class a firmly nonexpansive-type mapping. This class contains the classes of firmly nonexpansive mappings in Hilbert spaces an...
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A class of nonlinear operators in Banach spaces is proposed. We call each operator in this class a firmly nonexpansive-type mapping. This class contains the classes of firmly nonexpansive mappings in Hilbert spaces and resolvents of maximal monotone operators in Banach spaces. We study the existence and approximation of fixed points of firmly nonexpansive-type mappings in Banach spaces.
In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in [Chretien and Hero (19...
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In this paper we focus on the problem of identifying the index sets P(x) := {i \ x(i)>0}, N(x) := {i \ F-i(x)>0} and C(x) := {i \ x(i) = F-i(x)=0} for a solution x of the monotone nonlinear complementarity probl...
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In this paper we focus on the problem of identifying the index sets P(x) := {i \ x(i)>0}, N(x) := {i \ F-i(x)>0} and C(x) := {i \ x(i) = F-i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.
This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaido o-Isoda function is convex-concave, selected Nash equilibria cor...
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This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaido o-Isoda function is convex-concave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to design computational algorithms for finding such equilibria. To comply with some freedom of individual choice the algorithms developed here are fairly decentralized. However, since coupling constraints must be enforced, repeated coordination is needed while underway towards equilibrium. Particular instances include zero-sum, two-person games -or minimax problems that are convex-concave and involve convex coupling constraints.
In this paper, we propose a new rapid projection method for solving a class of linear complementarity problems based on matrix split technique and the idea of proximal point algorithm. The global convergence of the me...
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In this paper, we propose a new rapid projection method for solving a class of linear complementarity problems based on matrix split technique and the idea of proximal point algorithm. The global convergence of the method is analyzed. Numerical experiments show that the new method compared with some existing methods has more efficiency and robustness in solving kinds of linear complementarity problems and can be applied very easily. Numerical experiments also show that the new method for those problems is almost not sensitive to the parameters used in this method. (c) 2006 Published by Elsevier Inc.
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