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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2024 Volume 64, Number 4, Pages 605–613 (Mi zvmmf11736)

Papers published in the English version of the journal

Three-step approximation methods from continuous and discrete perspective for quasi-variational inequalities

N. Mijajlovića, M. Jaćimovićab

a University of Montenegro, Faculty of Science and Mathematics, 81000, Podgorica, Montenegro
b Montenegrin Academy of Sciences and Arts, 81000, Podgorica, Montenegro

Abstract: The objective of this manuscript is to study the convergence of three-step approximation methods for quasi-variational inequalities in the general case. First, we propose the three-step dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into a three-step iterative method, which we prove to converge also when it is applied to strongly-monotone quasi-variational inequalities. In addition, we show that linear convergence is guaranteed under strong-monotonicity.

Key words: quasi-variational inequalities, three-step method, dynamical system, rate of convergence.

Received: 12.09.2023
Revised: 23.10.2023
Accepted: 07.06.2024

Language: English


 English version:
Computational Mathematics and Mathematical Physics, 2024, 64:4, 605–613


© Steklov Math. Inst. of RAS, 2024