變分不等式的慣性次梯度外梯度算法

楊志　夏福全

摘要：在實Hilbert空間中提出求解單調變分不等式的慣性次梯度外梯度算法，其中變分不等式的可行集是一個光滑凸函數的水平集.新算法應用慣性加速技巧，迭代過程中對映射F賦值一次，并只需向兩個半空間作投影兩次.在適當的假設下，證明該算法的弱收斂性.新算法改進和推廣相關文獻中的相應結果.

關鍵詞：次梯度外梯度算法; 單調; Lipschitz連續; 慣性方法; 變分不等式

中圖分類號：O117; O178 文獻標志碼：A 文章編號：1001-8395（2023）05-0591-10

1預備知識

2算法

3收斂性分析

4數值結果

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An? Inertial Subgradient Extragradient Algorithm for Solving

Variational InequalitiesYANG Zhi，XIA Fuquan（School of Mathematical Sciences， Sichuan Normal University， Chengdu 610066， Sichuan）

Abstract：In this paper， we propose a new inertial subgradient extragradient algorithm for solving monotone variational inequalities in Hilbert space， where the feasible set of variational inequality is the level set of a smooth convex function. The new algorithm uses the inertial acceleration technique. The value of F is calculated once during per iteration， only needs to project to two half spaces twice. Under the appropriate assumptions， the weak convergence of the algorithm is proved. The new algorithm improves and generalizes the corresponding results in the relevant literature.

Keywords：subgradient extragradient algorithm; monotone; Lipschitz continuous; inertial method; variational inequalities

2020 MSC：65K15; 90C25; 90C33

（編輯陶志寧）