A modified Solodov-Svaiter method for solving nonmonotone variational inequality problems

In a very interesting paper ( SIAM J. Control Optim. 37(3): 765–776, 1999), Solodov and Svaiter introduced an effective projection algorithm with linesearch for finding a solution of a variational inequality problem (VIP) in Euclidean space. They showed that the iterative sequence generated by their...

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Bibliographic Details
Published inNumerical algorithms Vol. 90; no. 4; pp. 1715 - 1734
Main Authors Van Dinh, Bui, Manh, Hy Duc, Thanh, Tran Thi Huyen
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2022
Springer Nature B.V
Subjects
Algebra
Algorithms
Computer Science
Euclidean geometry
Euclidean space
Iterative methods
Mapping
Mathematical programming
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
47J20
49J40
90C33
Projection algorithm
Non-monotonicity
Armijo linesearch
Variational inequalities
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Summary:In a very interesting paper ( SIAM J. Control Optim. 37(3): 765–776, 1999), Solodov and Svaiter introduced an effective projection algorithm with linesearch for finding a solution of a variational inequality problem (VIP) in Euclidean space. They showed that the iterative sequence generated by their algorithm converges to a solution of (VIP) under the main assumption that the cost mapping is pseudomonotone and continuous. In this paper, we propose to modify this algorithm for solving variational inequality problems in which the cost mapping is not required to be satisfied any pseudomonotonicity. Moreover, we do not use the embedded projection methods as in methods used in literature and the linesearch procedure is not necessary when the cost mapping is Lipschitz. Several numerical examples are also provided to illustrate the efficient of the proposed algorithms.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-021-01248-w