In this research, we are interested about the monotone inclusion problems in the scope of the real Hilbert spaces by using an inertial forward-backward splittingalgorithm. In addition, we have discussed the applicati...
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In this research, we are interested about the monotone inclusion problems in the scope of the real Hilbert spaces by using an inertial forward-backward splittingalgorithm. In addition, we have discussed the application of this algorithm.
Monotone inclusion problems are crucial to solve engineering problems and problems arising in different branches of science. In this paper, we propose a novel two-step inertial Douglas-Rachford algorithm to solve the ...
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Monotone inclusion problems are crucial to solve engineering problems and problems arising in different branches of science. In this paper, we propose a novel two-step inertial Douglas-Rachford algorithm to solve the monotone inclusion problem of the sum of two maximally monotone operators based on the normal S-iteration method (Sahu, D.R.: Applications of the S-iteration process to constrained minimization problems and split feasibility problems. Fixed Point Theory 12(1), 187-204 (2011)). We have studied the convergence behavior of the proposed algorithm. Based on the proposed method, we develop an inertial primal-dual algorithm to solve highly structured monotone inclusions containing the mixtures of linearly composed and parallel-sum type operators. Finally, we apply the proposed inertial primal-dual algorithm to solve a highly structured minimization problem. We also perform a numerical experiment to solve the generalized Heron problem and compare the performance of the proposed inertial primal-dual algorithm to already known algorithms.
We introduce and investigate the convergence properties of an inertial forward-backward-forward splittingalgorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued mono...
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We introduce and investigate the convergence properties of an inertial forward-backward-forward splittingalgorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian operator. By making use of the product space approach, we expand it to the solving of inclusion problems involving mixtures of linearly composed and parallel-sum type monotone operators. We obtain in this way an inertial forward-backward-forward primal-dual splittingalgorithm having as main characteristic the fact that in the iterative scheme all operators are accessed separately either via forward or via backward evaluations. We present also the variational case when one is interested in the solving of a primal-dual pair of convex optimization problems with complexly structured objectives, which we also illustrate by numerical experiments in image processing.
We propose an inertial Douglas-Rachford splittingalgorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we form...
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We propose an inertial Douglas-Rachford splittingalgorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the inertial version of the Krasnosel'skii-Mann algorithm for approximating the set of fixed points of a nonexpansive operator, for which we also provide an exhaustive convergence analysis. By using a product space approach we employ these results to the solving of monotone inclusion problems involving linearly composed and parallel-sum type operators and provide in this way iterative schemes where each of the maximally monotone mappings is accessed separately via its resolvent. We consider also the special instance of solving a primal-dual pair of nonsmooth convex optimization problems and illustrate the theoretical results via some numerical experiments in clustering and location theory. (C) 2015 Elsevier Inc. All rights reserved.
In this article, we incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed to find the zeros of a maximally mono...
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In this article, we incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed to find the zeros of a maximally monotone operator in real Hilbert spaces. The convergence analysis relies on extended Fejer monotonicity techniques combined with the celebrated Opial Lemma. We also show that the classical hybrid proximal-extragradient algorithm and the inertial versions of the proximal point, the forward-backward and the forward-backward-forward algorithms can be embedded into the framework of the proposed iterative scheme.
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