| 摘要: |
| 变分不等式问题在经济金融、交通运输、数学规划、力学等领域都有着广泛的应用。 近年来,变分不等式问
题受到许多学者的研究,且这些研究主要集中在求解单调或者伪单调变分不等式问题。 文章在实希尔伯特空间
中,针对非单调变分不等式问题,提出了求解该问题的算法。 借助惯性原理和 Mann 型方法,构造了一个带 Armijo
线性搜索的修正惯性次梯度外梯度算法;在没有 Lipschitz 连续性的假设下,证明了由算法产生的迭代序列强收敛
于变分不等式问题的解,值得注意的是,定理的证明并没有要求映射的任何单调性假设;最后,给出了两个数值实
验,阐明了文章算法的有效性和优越性,所得结果推广和改进了许多最新的结果。 |
| 关键词: 变分不等式 次梯度外梯度算法 Armijo 线性搜索 强收敛 非单调 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Modified Inertial Subgradient Extragradient Algorithms for Solving Non-monotone Variational Inequality |
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FANG Zhenjie, LONG Xianjun
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School of Mathematics and Statistics Chongqing Technology and Business University Chongqing 400067 China
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| Abstract: |
| Variational inequality problems have a wide range of applications in economics and finance transportation
mathematical planning mechanics and other fields. In recent years the problem of variational inequalities has been
studied by many scholars and these studies have mainly focused on solving monotone or pseudo-monotone variational
inequalities. This article presented an algorithm for solving non-monotone variational inequality problems in real Hilbert
spaces. A modified inertial subgradient extragradient algorithm with Armijo linear search was constructed using the inertia
principle and Mann-type method. Under the assumption of non-Lipschitz continuity it was proved that the sequence of
iterations generated by the algorithm converged strongly to the solution of the variational inequality problems. It is worth
noting that the proof of the theorem does not require any monotonicity assumption for the mapping. Finally two numerical
experiments were given to illustrate the effectiveness and superiority of the algorithm in the paper. The results obtained
extend and improve many recent results. |
| Key words: variational inequalities subgradient extragradient algorithm Armijo linear search strong convergence non-monotone |
