We show that a strongly relatively nonexpansive sequence of mappings can be constructed from a given sequence of firmly nonexpansive-like mappings in a Banach space. Using this result, we study the problem of approxim...
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We show that a strongly relatively nonexpansive sequence of mappings can be constructed from a given sequence of firmly nonexpansive-like mappings in a Banach space. Using this result, we study the problem of approximating common fixed points of such a sequence of mappings.
In this paper, a parallel iterative algorithm is investigated for common zeros of a family of m-accretive operators. Strong convergence theorems are established in a reflexive Banach space.
In this paper, a parallel iterative algorithm is investigated for common zeros of a family of m-accretive operators. Strong convergence theorems are established in a reflexive Banach space.
In this paper, a regularization method for treating zero points of the sum of two monotone operators is investigated. Strong convergence theorems are established in the framework of Hilbert spaces.
In this paper, a regularization method for treating zero points of the sum of two monotone operators is investigated. Strong convergence theorems are established in the framework of Hilbert spaces.
In this article, we prove strong and weak convergence theorems of modified proximal point algorithms for finding a common element of the zero point of maximal monotone operators, the set of solutions of generalized mi...
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In this article, we prove strong and weak convergence theorems of modified proximal point algorithms for finding a common element of the zero point of maximal monotone operators, the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems and the fixed point set of relatively nonexpansive mappings in a Banach space under difference conditions. Our results modify and improve previous result of Li and Song. Mathematics Subject Classification 2000: 47H09;47H10.
In this paper, we introduce and analyze a new unified hybrid iterative method to compute the approximate solution of the general optimization problem defined over the set D = Fix(T) boolean AND Omega vertical bar GMEP...
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In this paper, we introduce and analyze a new unified hybrid iterative method to compute the approximate solution of the general optimization problem defined over the set D = Fix(T) boolean AND Omega vertical bar GMEP(Phi, Psi, phi)], where Fix(T) is the set of common fixed points of a family T = {T(t) : 0 <= t < infinity} of nonexpansive self-mappings on a Hilbert space H, and Omega vertical bar GMEP(Phi, Psi, phi)] is the set of solutions of the generalized mixed equilibrium problem (in short, GMEP). Such type of minimization problem is called the hierarchical minimization problem. We establish the strong convergence of the sequences generated by the proposed algorithm. Our strong convergence theorem extends, improves and unifies the previously known results in the literature. We also give a numerical example to illustrate our algorithm and results. (C) 2013 Elsevier B.V. All rights reserved.
The notion of quasi-Fejer monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notio...
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The notion of quasi-Fejer monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of variable metric algorithms, whereby the underlying norm is allowed to vary at each iteration. Applications to convex optimization and inverse problems are demonstrated. (c) 2012 Elsevier Ltd. All rights reserved.
In this paper we prove strong convergence of the Browder-Tikhonov regularization method and the regularization inertial proximal point algorithm to a solution of nonlinear ill-posed equations involving m-accretive map...
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In this paper we prove strong convergence of the Browder-Tikhonov regularization method and the regularization inertial proximal point algorithm to a solution of nonlinear ill-posed equations involving m-accretive mappings in real, reflexive, and strictly convex Banach spaces with a uniformly Gateaux differentiable norm without weak sequential continuous duality mapping.
We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion yaT(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Ba...
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We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion yaT(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove that they inherit the regularity properties of T, and vice versa. We analyze the cases when the mapping T is metrically regular and strongly regular.
This paper focuses on the proximalpoint regularization technique for a class of optimal control processes governed by affine switched systems. We consider switched control systems described by nonlinear ordinary diff...
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This paper focuses on the proximalpoint regularization technique for a class of optimal control processes governed by affine switched systems. We consider switched control systems described by nonlinear ordinary differential equations which are affine in the input. The affine structure of the dynamical models under consideration makes it possible to establish some continuity/approximability properties and to specify these models as convex control systems. We show that, for some classes of cost functionals, the associated optimal control problem (OCP) corresponds to a conventional convex optimization problem in a suitable Hilbert space. The latter can be reliably solved using standard first-order optimization algorithms and consistent regularization schemes. In particular, we propose a conceptual numerical approach based on the gradient-type method and classic proximalpoint techniques.
We introduce a regularized equilibrium problem in Banach spaces, involving generalized Received 14 April 2012 Bregman functions. For this regularized problem, we establish the existence and Accepted 20 July 2012 uniqu...
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We introduce a regularized equilibrium problem in Banach spaces, involving generalized Received 14 April 2012 Bregman functions. For this regularized problem, we establish the existence and Accepted 20 July 2012 uniqueness of solutions. These regularizations yield a proximal-like method for solving equilibrium problems in Banach spaces. We prove that the proximal sequence is an asymptotically solving sequence when the dual space is uniformly convex. Moreover, we MSC: prove that all weak accumulation points are solutions if the equilibrium function is lower semicontinuous in its first variable. We prove, under additional assumptions, that the proximal sequence converges weakly to a solution. (C) 2012 Elsevier Ltd. All rights reserved.
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