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Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications

JOURNAL OF GLOBAL OPTIMIZATION 2019年第3期73卷 637-657页

作者： Pham Ky Anh Trinh Ngoc Hai Vietnam Natl Univ Dept Math 334 Nguyen Trai Hanoi Vietnam Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam

In this paper, we introduce two self-adaptive algorithms for solving a class of non-Lipschitz equilibrium problems. These algorithms are very simple in the sense that at each step, they require only one projection onto a feasible set. Their convergence can be established under quite mild assumptions. More precisely, the weak (strong) convergence of the first algorithm is proved under the pseudo-paramonotonicity (strong pseudomonotonicity) conditions, respectively. Especially, the convexity in the second argument of the involving bifunction is not required. In the second algorithm, the weak convergence is established under the pseudomonotonicity. Moreover, it is proved that under some additional conditions, the solvability of the equilibrium problem is equivalent to the boundedness of the sequences generated by the proposed algorithms. Some applications to the optimization problems and variational inequality problems as well as to transport equilibrium problems are also considered.

关键词： Equilibrium problem Variational inequality Fixed point problem Solution existence Non-convex optimization self-adaptive algorithm

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self-adaptive algorithms with inertial effects for solving the split problem of the demicontractive operators

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2020年第1期114卷 40-40页

作者： Suparatulatorn, Raweerote Cholamjiak, Prasit Suantai, Suthep Chiang Mai Univ Fac Sci Dept Math Chiang Mai 50200 Thailand Univ Phayao Sch Sci Phayao 56000 Thailand Chiang Mai Univ Fac Sci Res Ctr Math & Appl Math Dept Math Chiang Mai 50200 Thailand

The purpose of this paper is to introduce two new versions of self-adaptive algorithms by using inertial effects for solving the split common fixed point problem of demicontractive operators in Hilbert spaces and prove its weak and strong convergences under some weakened assumptions. Furthermore, we provide numerical experiments to illustrate the convergence behavior and efficiency of our proposed algorithms.

关键词： Split common fixed point problem Demicontractive operator self-adaptive algorithm Inertial algorithm

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self-adaptive algorithmS FOR SOLVING CONVEX BILEVEL OPTIMIZATION PROBLEMS

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS

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JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS 2023年第1期2023卷

作者： Zhao, Bowen Duan, Peichao Civil Aviat Univ China Coll Sci Tianjin 300300 Peoples R China

In this paper, we present a self-adaptive algorithm and an inertial version for solving convex bilevel optimization problems. We establish the strong convergence of our proposed algorithms. The step-sizes in our algorithms for the inner level optimization problem are selected without prior knowledge of operator norms. A numerical experiment is included to illustrate the performances of our algorithms and some comparisons are present with related algorithms.

关键词： Convex bilevel optimization Inertial acceleration Moreau-Yosida approximate self-adaptive algorithm Split proximal algorithm

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New inertial self-adaptive algorithms for the split common null-point problem: application to data classifications

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2023年第1期2023卷 136-136页

作者： Promkam, Ratthaprom Sunthrayuth, Pongsakorn Kesornprom, Suparat Tanprayoon, Ekapak Rajamangala Univ Technol Thanyaburi RMUTT Fac Sci & Technol Dept Math & Comp Sci Pathum Thani 12110 Thailand Chiang Mai Univ Off Res Adm Chiang Mai 50200 Thailand

In this paper, we propose two inertial algorithms with a new self-adaptive step size for approximating a solution of the split common null-point problem in the framework of Banach spaces. The step sizes are adaptively updated over each iteration by a simple process without the prior knowledge of the operator norm of the bounded linear operator. Under suitable conditions, we prove the weak-convergence results for the proposed algorithms in p-uniformly convex and uniformly smooth Banach spaces. Finally, we give several numerical results in both finite- and infinite-dimensional spaces to illustrate the efficiency and advantage of the proposed methods over some existing methods. Also, data classifications of heart diseases and diabetes mellitus are presented as the applications of our methods.

关键词： p-uniformly convex Banach spaces Weak convergence Split common null-point problem Maximal monotone operator self-adaptive algorithm

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Two new self-adaptive algorithms for solving the split common null point problem with multiple output sets in Hilbert spaces

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JOURNAL OF FIXED POINT THEORY AND APPLICATIONS 2021年第2期23卷 16-16页

作者： Reich, Simeon Truong Minh Tuyen Technion Israel Inst Technol Dept Math IL-32000 Haifa Israel Thai Nguyen Univ Sci Dept Math & Informat Thai Nguyen Vietnam

To solve the split common null point problem with multiple output sets in Hilbert spaces, we introduce two new self-adaptive algorithms and prove strong convergence theorems for both of them.

关键词： Hilbert space metric projection nonexpansive mapping self-adaptive algorithm split common null point problem

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self-adaptive MRPBIL-DE for 6D robot multiobjective trajectory planning

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EXPERT SYSTEMS WITH APPLICATIONS 2019年 136卷 133-144页

作者： Bureerat, Sujin Pholdee, Nantiwat Radpukdee, Thana Jaroenapibal, Papot Khon Kaen Univ Fac Engn Sustainable & Infrastruct Res & Dev Ctr Dept Mech Engn Khon Kaen 40002 Thailand Khon Kaen Univ Fac Engn Dept Ind Engn Khon Kaen 40002 Thailand

This work presents self-adaptive multiobjective real-code population-based incremental learning hybridised with differential evolution (MRPBIL-DE) for solving a 6D robot trajectory planning multiobjective optimisation problem. The objective functions are assigned to minimise travelling time and minimise maximum jerk taking place during motion while the constraints are velocity, acceleration and jerk constraints. A five order polynomial function is used to represent a motion equation while the motion path is divided into two sub-paths;from initial to intermediate positions and from intermediate to final positions. The optimiser is used to find a set of design variables including joint positions, velocities and accelerations at intermediate positions, moving time from the initial to intermediate positions, and that from the intermediate to final positions. Several multiobjective meta-heuristics (MOMHs) along with the proposed algorithm are used to solve the trajectory optimisation problem of robot manipulators while their performances are investigated. The results indicated that the proposed algorithm is effective and efficient for multiobjective robot trajectory planning optimisation problem. The results obtained from such a method are set as the baseline for further study of robot trajectory planning optimisation. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Multiobjective meta-heuristic algorithm Robot trajectory planning multiobjective Optimisation self-adaptive algorithm Time-jerk minimisation

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A novel self-adaptive control strategy of frost prevention and retardation for air source heat pumps in winter conditions

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APPLIED MATHEMATICAL MODELLING 2020年 83卷 284-300页

作者： Tang, Jinchen Herman, Cila Gong, Guangcai Chinese Acad Sci Inst Engn Thermophys Beijing 100190 Peoples R China Johns Hopkins Univ Dept Mech Engn Baltimore MD 21218 USA Hunan Univ Civil Engn Coll Changsha 410082 Hunan Peoples R China

As frost accumulates on the heat exchanger surface with time, system operating performance will be dramatically degraded, and limit its use in climates susceptible to frost formation. A novel self-adaptive control strategy of frost prevention and retardation for air source heat pumps (ASHP) is introduced in this paper. The control strategy relies on a new thermodynamic model, which involves a Dimensionless Artificial Neural Network (DANN) correlation model describing frost accumulation for ASHP on the air-side of the fin-and-tube heat exchanger. The dimensionless parameters of this DANN model, including the ambient conditions, 6 commonly used refrigerants, and the geometric parameters of the heat exchanger, are considered in the model. To enhance the reliability of DANN, we develop a self-adaptive algorithm, including determining the optimal transfer algorithm and selecting the number of neurons in the hidden layer, for the DANN model. Results show a limited relative error (7.55%) between calculated values and experimental data, which help researchers and manufacturers analyze the complicated frosting process and design the new ASHPs more reasonably in different regions with different ambient conditions. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Dimensionless model Air source heat pump Frost accumulation Different refrigerants Artificial neural networks self-adaptive algorithm

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An algorithm for the split feasible problem and image restoration

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2020年第1期115卷 1-18页

作者： Suparatulatorn, Raweerote Charoensawan, Phakdi Poochinapan, Kanyuta Dangskul, Supreedee Chiang Mai Univ Adv Res Ctr Computat Simulat Fac Sci Chiang Mai 50200 Thailand Chiang Mai Univ Dept Math Fac Sci Chiang Mai 50200 Thailand CHE Ctr Excellence Math Si Ayutthaya Rd Bangkok 10400 Thailand

This paper proposes an accelerated algorithm for the split common fixed point problem, based on viscosity approximation methods and inertial effects. The main result will be applied to image restoration problems. This algorithm is constructed in such a way that its step sizes and the norm of a given linear operator are not related. Under some conditions, the strong convergence of the algorithm is obtained. Numerical investigations are carried out in order to illustrate high-performance of the present work, mainly using processing duration and the signal-to-noise ratio. It is also shown that this proposed algorithm is more efficient and effective than the published algorithm by Yao et al.

关键词： Split common fixed point problem Demicontractive operator self-adaptive algorithm Inertial algorithm Image restoration problem

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Accurate displacement measurement via a self-adaptive digital image correlation method based on a weighted ZNSSD criterion

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OPTICS AND LASERS IN ENGINEERING 2014年第1期52卷 75-85页

作者： Yuan, Yuan Huang, Jianyong Peng, Xiaoling Xiong, Chunyang Fang, Jing Yuan, Fan Peking Univ Coll Engn Beijing 100871 Peoples R China Duke Univ Dept Biomed Engn Durham NC 27708 USA

Digital image correlation (DIC) technique has been increasingly employed to implement surface deformation measurements in many engineering fields. Practically, it has been demonstrated that the choice of subset sizes exerts a strong influence on measurement results of DIC, especially when there exists locally larger deformation over the subsets involved. This paper proposes a novel subpixel registration algorithm with Gaussian windows to implicitly optimize the subset sizes by adjusting the shape of Gaussian windows in a self-adaptive fashion with the aid of a so-called weighted zero-normalized sum-of-squared difference correlation criterion. The feasibility and effectiveness of the self-adaptive algorithm are carefully verified through a set of well-designed synthetic speckle images, which indicates that the presented algorithm is able to greatly enhance the accuracy and precision of displacement measurements as compared with the traditional subpixel registration methods. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Deformation measurement Subpixel registration Subset size self-adaptive algorithm Gaussian window

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self-adaptive relaxed CQ algorithms for solving split feasibility problem with multiple output sets

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2024年第2期70卷 1441-1469页

作者： Tong, Xiaolei Ling, Tong Shi, Luoyi Tiangong Univ Sch Math Sci Tianjin 300387 Peoples R China Tiangong Univ Sch Software Tianjin 300387 Peoples R China

In this paper, we propose two new self-adaptive relaxed CQ algorithms to solve the split feasibility problem with multiple output sets, which involve the computation of projections onto half-spaces instead of the computation onto the closed convex sets. Our proposed algorithms with selection technique reduce the computation of projections. And then, as a generalization, we construct two new algorithms to solve the variational inequalities over the solution set of split feasibility problem with multiple output sets. More importantly, strong convergence of all proposed algorithms is proved under suitable conditions. Finally, we conduct numerical experiments to show the efficiency and accuracy of our algorithms compared to some existing results.

关键词： Split feasibility problem Multiple output sets Strong convergence Relaxed CQ algorithm self-adaptive algorithm

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