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An Algorithm for Finding a Common Solution for a System of Mixed Equilibrium Problem, Quasivariational Inclusion Problem, and Fixed Point Problem of Nonexpansive Semigroup [PDF]
Journal of Inequalities and Applications, 2010 We introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for nonexpansive semigroup, and the set of solutions of the quasi-variational inclusion ...
M. Liu, S. S. Chang, P. Zuo
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Abstract and Applied Analysis, 2014 We introduce and analyze a relaxed extragradient-like viscosity iterative algorithm for finding a solution of a generalized mixed equilibrium problem with constraints of several problems: a finite family of variational inequalities for inverse strongly ...
Lu-Chuan Ceng +3 more
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Iterative Galerkin discretizations for strongly monotone problems
Journal of Computational and Applied Mathematics, 2017 In this article we investigate a finite element formulation of strongly monotone quasi-linear elliptic PDEs in the context of fixed-point iterations. As opposed to Newton's method, which requires information from the previous iteration in order to linearise the iteration matrix (and thereby to recompute it) in each step, the alternative method used in ...
Congreve, Scott, Wihler, Thomas P.
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RAIRO - Operations Research, 2023 This paper introduces the concepts of strongly geodesic preinvexity, strongly η-invexity of order m, and strongly invariant η-monotonicity of order m on Riemannian manifolds. Additionally, it discusses an important characterization of these functions under a condition, known as Condition C (The Condition C is defined in Remark 1 of this article ...
Aklad Iqbal +2 more
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Strongly Nonexpansive Mappings Revisited: Uniform Monotonicity and Operator Splitting
SIAM Journal on Optimization, 2023 The correspondence between the class of nonexpansive mappings and the class of maximally monotone operators via the reflected resolvents of the latter has played an instrumental role in the convergence analysis of the splitting methods. Indeed, the performance of some of these methods, e.g., Douglas-Rachford and Peaceman-Rachford methods hinges on ...
Liu, Leon +2 more
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Iterative Methods for the Sum of Two Monotone Operators
Journal of Applied Mathematics, 2012 We introduce an iterative for finding the zeros point of the sum of two monotone operators. We prove that the suggested method converges strongly to the zeros point of the sum of two monotone operators.
Yeong-Cheng Liou
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Abstract and Applied Analysis, 2012 We prove the strong convergence theorems for finding a common element of the set of fixed points of a nonspreading mapping T and the solution sets of zero of a maximal monotone mapping and an α-inverse strongly monotone mapping in a Hilbert space. Manaka
Hongjie Liu +2 more
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Prevalent behavior of smooth strongly monotone discrete-time dynamical systems [PDF]
Proceedings of the American Mathematical Society, 2022 For C 1 C^{1} -smooth strongly monotone discrete-time dynamical systems, it is shown that “convergence to linearly stable cycles” is a prevalent asymptotic behavior in the measure-theoretic sense.
Wang, Yi, Yao, Jinxiang, Zhang, Yufeng
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Computer Research and Modeling, 2022 In this paper we propose three tensor methods for strongly-convex-strongly-concave saddle point problems (SPP). The first method is based on the assumption of higher-order smoothness (the derivative of the order higher than 2 is Lipschitz-continuous) and achieves linear convergence rate. Under additional assumptions of first and second order smoothness
Ostroukhov, Petr +3 more
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A Forward-Backward Projection Algorithm for Approximating of the Zero of the Sum of Two Operators
پژوهشهای ریاضی, 2020 Introduction One of the most important classes of mappings is the class of monotone mappings due to its various applications. For solving many important problems, it is required to solve monotone inclusion problems, for instance, evolution
Vahid Dadashi
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