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An iterative algorithm for approximating convex minimization problem

APPLIED MATHEMATICS AND COMPUTATION 2007年第1期188卷 648-656页

作者： Yao, Yonghong Liou, Yeong-Cheng Yao, Jen-Chih Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 804 Taiwan Cheng Shiu Univ Dept Informat Management Kaohsiung 833 Taiwan Tianjin Polytech Univ Dept Math Tianjin 300160 Peoples R China

We suggest and analyze an iterative algorithm without the assumption of any type of commutativity on an infinite family of nonexpansive mappings. We show that the proposed iterative algorithm converges to the unique minimizer of some quadratic function over the common fixed point sets of an infinite family of nonexoansive mappings. Our result extend and improve many results announced by many authors. (C) 2006 Elsevier Inc. All rights reserved.

关键词： nonexpansive mapping fixed point convex minimization problem iterative algorithm

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Iterative algorithms of generalized nonexpansive mappings and monotone operators with application to convex minimization problem

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2022年第3期68卷 1841-1868页

作者： Maldar, Samet Aksaray Univ Dept Math TR-68100 Aksaray Turkey

In this paper, we present some convergence results for various iterative algorithms built from Hardy-Rogers type generalized nonexpansive mappings and monotone operators in Hilbert spaces. We obtain some comparison results for the rates of convergence of these algorithms to the solution of variational inequality problem including Hardy-Rogers type generalized nonexpansive mappings and monotone operators. A numerical example is given to validate these results. We apply the iterative algorithms handled herein to solve convex minimization problem and illustrate this result by providing a non-trivial numerical example. The presented results considerably improve the corresponding results in Ali et al. Comput Appl Math 39:74, 2020. https://***/10.1007/s40314-020-1101-4).

关键词： Fixed point Variational inequality Monotone operators Generalized nonexpansive mappings convex minimization problem

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An iterative algorithm for fixed point problem and convex minimization problem with applications

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FIXED POINT THEORY AND APPLICATIONS 2015年第1期2015卷 1-17页

作者： Cai, Gang Shehu, Yekini Chongqing Normal Univ Coll Math Sci Chongqing 401331 Peoples R China Univ Nigeria Dept Math Nsukka Nigeria

In this paper we prove the strong convergence of an iterative sequence for finding a common element of the fixed points set of a strictly pseudocontractive mapping and the solution set of the constrained convex minimization problem for a convex and continuously Fr,chet differentiable functional in a real Hilbert space. We apply our result to solving the split feasibility problem and the convexly constrained linear inverse problem involving the fixed point problem for a strictly pseudocontractive mapping in a real Hilbert space.

关键词： convex minimization problem k-strictly pseudo contractive mapping strong convergence Hilbert spaces

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Proximal point algorithms for solving convex minimization problem and common fixed points problem of asymptotically quasi-nonexpansive mappings in CAT(0) spaces with convergence analysis

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NUMERICAL ALGORITHMS 2018年第3期78卷 827-845页

作者： Pakkaranang, Nuttapol Kumam, Poom Cho, Yeol Je KMUTT Fac Sci Dept Math KMUTTFixed Point Res Lab Room SCL 802 Fixed Point LabSci Lab Bldg Bangkok 10140 Thailand KMUTT KMUTT Fixed Point Theory & Applicat Res Grp KMUTT Fac Sci Theoret & Computat Sci Ctr TaCS Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand Gyeongsang Natl Univ Dept Math Educ Jinju 660701 South Korea Gyeongsang Natl Univ RINS Jinju 660701 South Korea China Med Univ Ctr Gen Educ Taichung 40402 Taiwan

In this paper, we introduce the modified proximal point algorithm for common fixed points of asymptotically quasi-nonexpansive mappings in CAT(0) spaces and also prove some convergence theorems of the proposed algorithm to a common fixed point of asymptotically quasi-nonexpansive mappings and a minimizer of a convex function. The main results in this paper improve and generalize the corresponding results given by some authors. Moreover, we then give numerical examples to illustrate and show efficiency of the proposed algorithm for supporting our main results.

关键词： Proximal point algorithm convex minimization problem Common fixed point Asymptotically quasi-nonexpansive mapping CAT(0) spaces

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Alternating minimization algorithms for convex minimization problem with application to image deblurring and denoising

Alternating minimization algorithms for convex minimization ...

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International Conference on Control, Artificial Intelligence, Robotics and Optimization (ICCAIRO)

作者： Padcharoen, Anantachai Kumam, Poom Chaipunya, Parin Kumam, Wiyada Siricharoen, Punnarai Thounthong, Phatiphat KMUTT Fac Sci Dept Math 126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT Fac Sci Theoret & Computat Sci Ctr TaCS Fixed Point Theory & Applicat Res Grp Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand Rajamangala Univ Technol Thanyaburi RMUTT Fac Sci & Technol Dept Math & Comp Sci Program Appl Stat Thanyaburi 12110 Pathumthani Thailand KMUTT Fac Sci Theoret & Computat Sci Ctr TaCS Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand King Mongkuts Univ Technol Fac Tech Educ Dept Teacher Training Elect Engn Renewable Energy Res Ctr Bangkok 10800 Thailand

ISBN: (纸本)9781538695760

In this paper, we propose algorithm to restore blurred and noisy images based on the discretized total variation minimization technique. The proposed method is based on an alternating technique for image deblurring and denoising. Start by finding an approximate image using a Tikhonov regularization method. This corresponds to a deblurring process with possible artifacts and noise remaining. In the denoising step, we use fast iterative shrinkage-thresholding algorithm (SFISTA) or fast gradient-based algorithm (FGP). Besides, we prove the convergence of the proposed algorithm. Numerical results demonstrate the efficiency and viability of the proposed algorithm to restore the degraded images.

关键词： Alternating minimization algorithms convex minimization problem image deblurring

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Algorithms for zeros of two accretive operators for solving convex minimization problems and its application to image restoration problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2019年 354卷 471-495页

作者： Kitkuan, Duangkamon Kumam, Poom Padcharoen, Anantachai Kumam, Wiyada Thounthong, Phatiphat KMUTT Fac Sci Fixed Point Lab KMUTTFixed Point Res LabDept Math Room SCL 802Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT Fac Sci Theoret & Computat Sci Ctr TaCS Fixed Point Theory & Applicat Res Grp Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand Rajamangala Univ Technol Thanyaburi RMUTT Fac Sci & Technol Dept Math & Comp Sci Program Appl Stat Thanyaburi 12110 Pathumthani Thailand King Mongkuts Univ North Bankok Fac Tech Educ Dept Teacher Training Elect Engn Renewable Energy Res Ctr Bangkok 108000 Thailand

In this paper, a new viscosity iterative method minimization algorithm for image restoration algorithm is proposed. Based on a new viscosity iteration, the algorithm for finding the common zeros of two accretive operators in the framework of uniformly smooth Banach spaces. Moreover, the strong convergence theorems for the iterative algorithms and an example is proposed which shows the validity of main theorem are proved. The results of this paper are improved and extended of the corresponding ones announced by many others and we also applied our result to solve a convex minimization problem and Gateaux differentiable EPs and Variational Inequality. Experiment results show that the proposed algorithms outperform some other methods. Finally, we give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for applying to solve the image deblurring and image recovery problems. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Common zeros Accretive operator convex minimization problem Image recovery problems Douglas-Rachford-algorithm Forward-backward algorithm

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The conjugate gradient method for split variational inclusion and constrained convex minimization problems

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APPLIED MATHEMATICS AND COMPUTATION 2016年 290卷 426-438页

作者： Che, Haitao Li, Meixia Weifang Univ Sch Math & Informat Sci Weifang 261061 Shandong Peoples R China

In this paper, we introduce and study a new viscosity approximation method based on the conjugate gradient method and an averaged mapping approach for finding a common element of the set of solutions of a constrained convex minimization problem and the set of solutions of a split variational inclusion problem. Under suitable conditions, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of the split variational inclusion problem and the set of solutions of the constrained convex minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area. Finally, preliminary numerical results indicate the feasibility and efficiency of the proposed methods. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Split variational inclusion problem Fixed point problem convex minimization problem Viscosity approximation method Conjugate gradient method

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Generalized Halpern-type forward-backward splitting methods for convex minimization problems with application to image restoration problems

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OPTIMIZATION 2020年第7-8期69卷 1557-1581页

作者： Kitkuan, Duangkamon Kumam, Poom Martinez-Moreno, Juan KMUTT KMUTTFixed Point Res Lab Fixed Point Lab Fac Sci Room SCL 802Sci Lab Bldg Bangkok Thailand KMUTT Dept Math Fac Sci Room SCL 802Sci Lab Bldg Bangkok Thailand KMUTT Ctr Excellence Theoret & Computat Sci TaCS CoE Fac Sci Sci Lab Bldg Bangkok Thailand Univ Jaen Fac Expt Sci Dept Math Jaen Spain

In this work, our interest is to investigate the monotone inclusion problem in the framework of real Hilbert spaces. For solving the inclusion problem, we propose a composite iteration for approximating a zero of sum of two operators. We prove its strong convergence under some mild conditions. Finally, we provide a number of applications to convex minimization and image restoration problems including numerical experiments to support our main theorem.

关键词： Forward-backward splitting method inclusion problem convex minimization problem monotone operator Hilbert spaces

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New iterative methods for nonlinear operators as concerns convex programming applicable in differential problems, image deblurring, and signal recovering problems

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2023年第3期46卷 3332-3355页

作者： Chairatsiripong, Chonjaroen Yambangwai, Damrongsak Thianwan, Tanakit Univ Phayao Sch Sci Phayao 56000 Thailand

In this paper, using sunny nonexpansive retractions, which are different from the metric projection in Banach spaces, a new type of study regarding the iterative methods in view of two quasi-nonexpansive nonself mappings is presented. We also give the convergence analysis for the proposed method in the background of uniformly convex Banach spaces. Moreover, we apply our results to find solutions of common zeros of accretive operators, convexly constrained least square problems, and convex minimization problems. Furthermore, we also discuss novel applications of these methods to differential problems, image deblurring, and signal recovering problems.

关键词： convexly constrained least square problem convex minimization problem image deblurring problem signal recovering problem Sunny nonexpansive retract

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On solving the minimization problem and the fixed-point problem for a finite family of non-expansive mappings in CAT(0) spaces

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OPTIMIZATION METHODS & SOFTWARE 2018年第2期33卷 311-321页

作者： Cuntavepanit, Asawathep Phuengrattana, Withun Mahidol Univ Kanchanaburi Campus Div Sci & Liberal Arts Kanchanaburi Thailand Nakhon Pathom Rajabhat Univ Fac Sci & Technol Dept Math Nakhon Pathom Thailand Nakhon Pathom Rajabhat Univ Inst Res & Dev Res Ctr Pure & Appl Math Nakhon Pathom Thailand

In this paper, we propose a new modified proximal point algorithm for a finite family of non-expansive mappings in the framework of CAT(0) spaces. We establish -convergence and strong convergence theorems under some m... 详细信息

关键词： convex minimization problem fixed-point problems proximal point algorithm nonexpansive mappings CAT(0) spaces

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