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| Abstract: |
| Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method about classical variational inequality in a real Hilbert interspace. By analyzing the operator's partial message, the proposed method designs a non-monotonic step length strategy which requires no line search and is independent of the value of Lipschitz constant, and is extended to solve the problem of pseudomonotone variational inequality. Meanwhile, the method requires merely one map value and a projective transformation to the practicable set at every iteration. In addition, without knowing the Lipschitz constant for interrelated mapping, weak convergence is given and R-linear convergence rate is established concerning algorithm. Several numerical results further illustrate that the method is superior to other algorithms. |
| Key words: variational inequality subgradient extragradient method non-monotonic stepsize strategy pseudomonotone mapping |
| DOI：10.11916/j.issn.1005-9113.2020026 |
| Clc Number:O221.2 |
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| Descriptions in Chinese: |
| 伪单调变分不等式的修正次梯度外梯度方法 程佳佳，刘红卫 (西安电子科技大学 数学与统计学院，西安 710126) 中文说明：多种求解变分不等式问题的方法中次梯度外梯度法是非常重要的一种方法。本文提出实Hilbert空间中关于经典变分不等式的修正的次梯度外梯度法。通过分析算子的局部信息，介绍一种不需要线搜索且不依赖于利普希茨常数取值的非单调步长策略，并将其推广到求解伪单调变分不等式问题。同时，该方法在每次迭代中只需要一个函数值和一个到可行集的投影。此外，在相关映射的利普希茨常数未知的情况下，给出了算法的弱收敛性和R-线性收敛率。数值结果进一步说明该方法优于其它算法。 关键词：变分不等式、次梯度外梯度法、非单调步长策略、伪单调映射 |
