哈达玛流形中伪单调变分不等式问题的新曾外梯度方法

Fixed Point Theory and Applications Pub Date : 2021-02-22 DOI:10.1186/s13663-021-00689-1

Konrawut Khammahawong, Poom Kumam, Parin Chaipunya, Somyot Plubtieng

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引用次数: 0

摘要

我们提出了曾外梯度方法，用于寻找哈达玛流形中与伪单调向量场相关的变分不等式问题的解。在伪单调向量场和 Lipschitz 连续向量场等标准假设条件下，我们证明了由所提方法生成的任何序列，只要存在，都会收敛到变分不等式问题的解。此外，我们还给出了一些数值实验来说明我们的主要结果。

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New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds

We propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.

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Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.