求解单调变分不等式和不动点问题的惯性修正Tseng的外加算法

IF 1.1 Q1 MATHEMATICS

Journal of Nonlinear Functional Analysis Pub Date : 2020-01-01 DOI:10.23952/jnfa.2020.35

M. Tian, XU Gang

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引用次数: 12

摘要

针对实数Hilbert空间中拟非扩张映射的单调变分不等式和不动点问题，提出了两种结合惯性Tseng法和混合投影法的新算法。在适当的条件下，建立了弱收敛定理和强收敛定理。最后，通过数值实验验证了所提算法的有效性和优越性。

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Inertial modified Tseng’s extragradient algorithms for solving monotone variational inequalities and fixed point problems

For solving monotone variational inequalities and fixed point problems of a quasi-nonexpansive mapping in real Hilbert spaces, we introduce two new algorithms which combine the inertial Tseng’s extragradient method and the hybrid-projection method, respectively. Weak and strong convergence theorems are established under some appropriate conditions. Finally, we provide some numerical experiments to show the effectiveness and advantages of the proposed algorithms.

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来源期刊

Journal of Nonlinear Functional Analysis Multiple-

CiteScore

2.40

自引率

0.00%

发文量

期刊介绍： Journal of Nonlinear Functional Analysis focuses on important developments in nonlinear functional analysis and its applications with a particular emphasis on topics include, but are not limited to: Approximation theory; Asymptotic behavior; Banach space geometric constant and its applications; Complementarity problems; Control theory; Dynamic systems; Fixed point theory and methods of computing fixed points; Fluid dynamics; Functional differential equations; Iteration theory, iterative and composite equations; Mathematical biology and ecology; Miscellaneous applications of nonlinear analysis; Multilinear algebra and tensor computation; Nonlinear eigenvalue problems and nonlinear spectral theory; Nonsmooth analysis, variational analysis, convex analysis and their applications; Numerical analysis; Optimal control; Optimization theory; Ordinary differential equations; Partial differential equations; Positive operator inequality and its applications in operator equation spectrum theory and so forth; Semidefinite programming polynomial optimization; Variational and other types of inequalities involving nonlinear mappings; Variational inequalities.