A modified Solodov-Svaiter method for solving nonmonotone variational inequality problems (cont.)
Báo cáo viên: Bùi Văn Định

Thời gian: 9h, Thứ 4 ngày 14/4/2021

Địa điểm: Phòng 302, Nhà A5, Viện Toán học

Tóm tắt: 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 satisfy 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 efficiency of the proposed algorithms.