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DOI: 10.23952/cot.2020.2
Received November 27, 2019; Accepted January 31, 2020; Published February 14, 2020
Abstract. In this paper, we introduce asymptotic inertial subgradient extragradient algorithms with a line-search process for solving a variational inequality problem (VIP) with pseudomonotone and Lipschitz continuous mappings and a common fixed-point problem (CFPP) of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. The proposed algorithms are based on the inertial subgradient extragradient method with a line-search process, hybrid steepest-descent methods, viscosity approximation methods, Mann iteration methods and asymptotically nonexpansive mappings. Under mild conditions, we prove strong convergence of the proposed algorithms.
How to Cite this Article:
Lu-Chuan Ceng, Asymptotic inertial subgradient extragradient approach for pseudomonotone variational inequalities with fixed point constraints of asymptotically nonexpansive mappings, Communications in Optimization Theory, Vol. 2020 (2020), Article ID 2, pp. 1-21.