Article
Mathematics, Applied
Weibo Guan, Wen Song
Summary: This paper introduces a non-traditional forward-backward splitting method for minimizing the sum of two convex functions in Banach space, where one function is smooth and the other is non-smooth. Different convergence estimates are established under different stepsize assumptions.
Article
Operations Research & Management Science
Yamin Wang, Fenghui Wang, Haixia Zhang
Summary: This paper focuses on the Forward-Backward algorithm (FBA) in Banach spaces that are uniformly convex and q-uniformly smooth. Two viscosity FBAs are introduced, one of which has a weakly contractive mapping, generalizing many previous results. The paper also establishes their strong convergences under more general conditions.
Article
Mathematics, Applied
Hong-Kun Xu, Najla Altwaijry, Imtithal Alzughaibi, Souhail Chebbi
Summary: The viscosity approximation method is extended to accretive operators in a uniformly convex and/or uniformly Gateaux differentiable Banach space in order to find a zero of an m-accretive operator and of the sum of two m-accretive operators. The strong convergence of the VAM algorithms is proved in all cases, and the limit of the iterates is identified as the unique sunny nonexpansive retraction onto to the zero set of the operator.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2022)
Article
Operations Research & Management Science
Yinglin Luo, Bing Tan, Songxiao Li
Summary: In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and q-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.
Article
Operations Research & Management Science
Prasit Cholamjiak, Nattawut Pholasa, Suthep Suantai, Pongsakorn Sunthrayuth
Summary: The paper introduces a generalized viscosity explicit method for finding zeros of the sum of two accretive operators in the framework of Banach spaces. The strong convergence theorem of such method is proved under certain parameter assumptions. Applications of the method to various problems such as variational inequality, convex minimization, and split feasibility are demonstrated through numerical experiments.
Article
Operations Research & Management Science
Wei-Bo Guan, Wen Song
Summary: This paper proposes a method for solving nonsmooth optimization problems in Banach spaces without assuming the standard Lipschitz continuity of the gradient. The weak convergence of the iterative sequence generated by this method is proven, and further convergence with an asymptotic rate of 1/n to the optimal value is proven under the assumption of boundedness of the iterative sequence.
OPTIMIZATION LETTERS
(2022)
Article
Mathematics, Applied
Timilehin Opeyemi Alakoya, Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomo
Summary: This paper introduces a new algorithm for approximating common solutions of infinite families of inclusion problems and accretive variational inequality problems, achieving strong convergence and perturbation resilience. The algorithm is also applied to solve nonlinear integro-differential equations with generalized p-Laplacian operator.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2022)
Article
Operations Research & Management Science
A. U. Bello, C. C. Okeke, M. Isyaku, M. T. Omojola
Summary: The paper proves the weak convergence of the forward-reflected-backward splitting method to a solution of the inclusion of the sum of two monotone operators in a real 2-uniformly convex Banach space E with topological dual E*. A variant of the method is also introduced where the step size is independent of the Lipschitz constant of one of the operators. Furthermore, the results extend and complement various existing findings in the literature, and numerical illustrations are provided to demonstrate the applicability and efficiency of the proposed method.
Article
Mathematics, Applied
Pronpat Peeyada, Hemen Dutta, Kanokwatt Shiangjen, Watcharaporn Cholamjiak
Summary: This paper proposes a modified forward-backward splitting algorithm with an inertial technique to solve the monotone variational inclusion problem. The algorithm is weakly convergent in Hilbert space, and a new step size is introduced to accelerate convergence. Experimental results support the effectiveness of the algorithm in infinite dimensional spaces, and it is applied to breast cancer prediction.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Jun Yang, Prasit Cholamjiak, Pongsakorn Sunthrayuth
Summary: In this paper, we introduce two modified algorithms for solving monotone inclusion problem in Banach spaces. We establish the convergence results under certain conditions. Furthermore, we apply our results to other problems and conduct numerical experiments with comparisons to related algorithms.
Article
Operations Research & Management Science
Wei-Bo Guan, Wen Song
Summary: In this paper, the forward-backward splitting method is extended to Banach spaces for the minimization of the sum of two functions. The functional values of the sequences generated by this method converge asymptotically to the optimal value with a rate of n(1-p), and linear convergence is established under an error bound assumption.
OPTIMIZATION LETTERS
(2021)
Article
Mathematics, Applied
Prasit Cholamjiak, Dang Van Hieu, Yeol Je Cho
Summary: In this paper, a relaxed version of the modified forward-backward splitting method (MFBSM) is introduced for solving a variational inclusion problem of the sum of two operators in Hilbert spaces. The algorithm uses variable step-sizes and is shown to converge with a linear rate. Another relaxed algorithm, which combines the first one with the inertial method, is proposed and analyzed for convergence. Several numerical experiments demonstrate the convergence of new algorithms and compare them with others.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics
Yanlai Song, Mihai Postolache
Summary: This paper presents a new algorithm for solving the quasi-variational inclusion problem and the variational inequality problem, proving the convergence of the algorithm and demonstrating the results through numerical examples.
Article
Computer Science, Artificial Intelligence
Damrongsak Yambangwai, Suhel Ahmad Khan, Hemen Dutta, Watcharaporn Cholamjiak
Summary: The paper introduces an advanced algorithm for approximating solutions of variational inclusion problems, achieving strong convergence results in real Hilbert spaces and demonstrating better convergence rates compared to other algorithms. The algorithm is not only effective for image recovery, but also shows promise in handling common blur effects.
Article
Operations Research & Management Science
Truong Minh Tuyen, Ratthaprom Promkam, Pongsakorn Sunthrayuth
Summary: This paper studies the generalized monotone quasi-inclusion problem and proposes a forward-backward splitting method to solve the problem. By applying the Bregman distance function, the strong convergence of the algorithm is proven and applied to the variational inequality problem. Numerical examples demonstrate the performance of the algorithm.
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Mathematics, Applied
Genaro Lopez-Acedo, Bozena Piatek
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Operations Research & Management Science
David Ariza-Ruiz, Genaro Lopez-Acedo, Adriana Nicolae
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Mathematics
David Ariza-Ruiz, Aurora Fernandez-Leon, Genaro Lopez-Acedo, Adriana Nicolae
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Operations Research & Management Science
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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
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Jinhua Wang, Chong Li, Genaro Lopez, Jen-Chih Yao
SIAM JOURNAL ON OPTIMIZATION
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Mathematics, Applied
Genaro Lopez, Victoria Martin-Marquez, Fenghui Wang, Hong-Kun Xu
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Jinhua Wang, Chong Li, Genaro Lopez, Jen-Chih Yao
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Mathematics, Applied
Vittorio Colao, Genaro Lopez, Giuseppe Marino, Victoria Martin-Marquez
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(2012)
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Mathematics, Applied
David Ariza-Ruiz, Chong Li, Genaro Lopez-Acedo
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Mathematics, Applied
J. S. He, D. H. Fang, G. Lopez, C. Li
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
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Mathematics
David Ariza-Ruiz, Laurentiu Leustean, Genaro Lopez-Acedo
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2014)
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Mathematics, Applied
Genaro Lopez-Acedo, Bozena Platek
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2016)
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Mathematics, Applied
David Ariza-Ruiz, Genaro Lopez-Acedo, Victoria Martin-Marquez
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2014)
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Mathematics, Applied
David Ariza-Ruiz, Antonio Jimenez-Melado, Genaro Lopez-Acedo
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
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Mathematics, Applied
David Ariza-Ruiz, Eyvind Martol Briseid, Antonio Jimenez-Melado, Genaro Lopez-Acedo
FIXED POINT THEORY
(2013)