楊志　夏福全

摘要：在實(shí)Hilbert空間中提出求解單調(diào)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(gè)光滑凸函數(shù)的水平集.新算法應(yīng)用慣性加速技巧，迭代過(guò)程中對(duì)映射F賦值一次，并只需向兩個(gè)半空間作投影兩次.在適當(dāng)?shù)募僭O(shè)下，證明該算法的弱收斂性.新算法改進(jìn)和推廣相關(guān)文獻(xiàn)中的相應(yīng)結(jié)果.

關(guān)鍵詞：次梯度外梯度算法; 單調(diào); Lipschitz連續(xù); 慣性方法; 變分不等式

中圖分類號(hào)：O117; O178 文獻(xiàn)標(biāo)志碼：A 文章編號(hào)：1001-8395（2023）05-0591-10

1預(yù)備知識(shí)

2算法

3收斂性分析

4數(shù)值結(jié)果

參考文獻(xiàn)

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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）