Inertial extragradient methods for solving pseudomonotone variational inequalities with non-Lipschitz mappings and their optimization applications
Bing Tan, Sun Young Cho, N An, N Nam, X Qin, A Khan, D Motreanu, D Sahu, J Yao, M Verma, K Shukla, Q Ansari, M Islam, J Yao, G Korpelevich, A Iusem, M Solodov, P Tseng, A Iusem, B Svaiter, M Solodov, B Svaiter, B He, P Tseng, Y Censor, A Gibali, S Reich, Y Malitsky, P Vuong, Y Shehu, Y Shehu, P Cholamjiak, Y Shehu, Q Dong, D Jiang, D Thong, A Gibali, D Thong, Y Shehu, O Iyiola, D Thong, Y Shehu, O Iyiola, S Reich, D Thong, Q Dong, X Li, V Dung, B Polyak, Y Shehu, O Iyiola, X Li, Q Dong, Y Shehu, X Li, Q Dong, L Liu, X Qin, B Tan, S Xu, S Li, B Tan, J Fan, S Li, Z Zhou, B Tan, S Li, S Denisov, V Semenov, L Chabak, A Iusem, R Otero, Y He, R Cottle, J Yao, S Saejung, P Yotkaew, A Gibali, D Thong, P Tuan, A Beck, N Guttmann-Beck, E Khoroshilova, J Preininger, P Vuong, J Bonnans, A Festa, A Pietrus, T Scarinci, V Veliov
Abstract
In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces.Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters.Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.