Inertial extragradient algorithms for strongly pseudomonotone variational inequalities

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:341

Article

Duong Viet Thong¹  Dang Van Hieu² 

[1] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[2] Coll Air Force, Dept Math, Nha Trang City, Vietnam

关键词: Variational inequality problem;    Strongly pseudomonotone operator;    Subgradient extragradient method;    Projection method;    Inertial method;    Tseng's extragradient;   

DOI  :  10.1016/j.cam.2018.03.019

来源: Elsevier

【 摘 要 】

The purpose of this paper is to study and analyze two different kinds of inertial type iterative methods for solving variational inequality problems involving strongly pseudomonotone and Lipschitz continuous operators in Hilbert spaces. The projection method is used to design the algorithms which can be computed more easily. The construction of solution approximations and the proof of convergence of the algorithms are performed without prior knowledge of the modulus of strong pseudomonotonicity and the Lipschitz constant of cost operator. Instead of that, the algorithms use variable stepsize sequences which are diminishing and non-summable. The numerical behaviors of the proposed algorithms on a test problem are illustrated and compared with several previously known algorithms. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free