求解Hilbert空间中双层分裂变分不等式问题的修正亚梯度外聚方法

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2023-07-18 DOI:10.1007/s40306-023-00508-2

Le Huynh My Van, Dang Le Thuy, Tran Viet Anh

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引用次数: 0

摘要

在这项工作中，我们提出了一种新的方法来解决Hilbert空间中的双层分裂变分不等式问题。该方法的灵感来自于求解单调变分不等式问题的次梯度超梯度方法。在不知道Lipschitz的任何信息和映射的强单调常数的情况下，证明了求解这种BSVIP的算法的强收敛定理。此外，我们不需要任何关于给定有界线性算子的范数的先验信息。考虑特殊情况。给出了两个数值例子来说明我们算法的性能。

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Modified Subgradient Extragradient Methods for Solving Bilevel Split Variational Inequality Problems in Hilbert Spaces

In this work, we propose a new method for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. The proposed method is inspired by the subgradient extragradient method for solving a monotone variational inequality problem. A strong convergence theorem for an algorithm for solving such a BSVIP is proved without knowing any information of the Lipschitz and strongly monotone constants of the mappings. Moreover, we do not require any prior information regarding the norm of the given bounded linear operator. Special cases are considered. Two numerical examples are given to illustrate the performance of our algorithm.

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来源期刊

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.