A two-step inertial method with a new step-size rule for quasimonotone variational inequalities in Hilbert spaces
Optimization Eruditorum, Volume 2, Issue 3, December 2025, Pages 184–199
JIAN-WEN PENG
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, People’s Republic of China
JUN-JIE LUO
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, People’s Republic of China
ABUBAKAR ADAMU
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, People’s Republic of China
Near East University, TRNC Mersin 10, Nicosia 99138, Turkey
Abstract
In this paper, a two-step inertial Tseng extragradient method involving self-adaptive and Armijo-like step sizes is introduced for solving variational inequalities with a quasimonotone and Lipschitz cost function in the setting of a real Hilbert space. Weak convergence of the sequence generated by the proposed algorithm is proved. An interesting feature of the proposed algorithm is its ability to select the better step size between the self-adaptive and Armijo-like options at each iteration step. Finally, the algorithm accelerates and complements several existing iterative algorithms for solving variational inequalities in Hilbert spaces.
Cite this Article as
Jian-Wen Peng, Jun-Jie Luo, and Abubakar Adamu, A two-step inertial method with a new step-size rule for quasimonotone variational inequalities in Hilbert spaces, Optimization Eruditorum, 2(3), 184–199, 2025