Weak and strong convergence of a modified adaptive generalized Popov's algorithm for solving variational inequality problems

• Published in: Optimization Vol. 73; no. 8; pp. 2695 - 2720
• Main Authors: Wang, Yuanheng, Gao, Yidan, Jiang, Bingnan
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.08.2024; Taylor & Francis LLC
• Subjects: Adaptive algorithms; Convergence; generalized Popov's method; Hilbert space; Mathematical analysis; Operators (mathematics); Quasi-monotone operator; strongly pseudo-monotone property; variational inequality problem; weak and strong convergence

In this paper, we introduce a modified adaptive step-size algorithm by basing a generalized Popov's method to solve variational inequality problems in a real Hilbert space. The algorithm only needs to act on the operator once time in each iteration, which greatly reduces the calculation time an...