求解Hilbert空间不动点集上的非单调平衡问题的一种外聚型算法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-19 DOI:10.1016/j.cnsns.2024.108547

Lanmei Deng , Rong Hu , Ya-Ping Fang

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引用次数: 0

摘要

给出了求解Hilbert空间中非扩张映射不动点集上的非单调非lipschitzian平衡问题的一种外聚型算法。得到了该算法生成的序列弱收敛于问题的一个解。弱收敛性不要求所涉及的平衡函数的单调性和Lipschitz连续性。这是在每次迭代时将当前点投影到可行集的收缩凸子集上并采用带次梯度的armijo型线研究的结果。数值行为表明了该算法的有效性。

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An extragradient-type algorithm for solving a nonmonotone equilibrium problem over the fixed point set in a Hilbert space

We present an extragradient-type algorithm for solving a nonmonotone and non-Lipschitzian equilibrium problem over the fixed point set of a nonexpansive mapping in a Hilbert space. We obtain that the sequence generated by the presented algorithm converges weakly to a solution of the problem. The weak convergence does not require any monotonicity and Lipschitz continuity of the involved equilibrium function. This is a result of projecting the current point onto shrinking convex subsets of the feasible set at each iteration and employing an Armijo-type linesearch with subgradient. The numerical behavior has shown the efficiency of the proposed algorithm.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.