New extragradient-like algorithms for strongly pseudomonotone variational inequalities

Dang Hieu () and Duong Viet Thong ()
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Dang Hieu: College of Air Force
Duong Viet Thong: National Economics University

Journal of Global Optimization, 2018, vol. 70, issue 2, No 5, 385-399

Abstract: Abstract The paper considers two extragradient-like algorithms 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 than the regularized method. The construction of solution approximations and the proof of convergence of the algorithms are performed without the prior knowledge of the modulus of strong pseudomonotonicity and the Lipschitz constant of the 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 those of several previously known algorithms.

Keywords: Variational inequality problem; Monotone operator; Pseudomonotone operator; Strongly monotone operator; Strongly pseudomonotone operator; Extragradient method; Subgradient extragradient method; Projection method; 65Y05; 65K15; 68W10; 47H05; 47H10 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10898-017-0564-3

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