Modified Tseng’s Extragradient Method for Solving Variational Inequality Problems and Fixed Point Problems with Applications in Optimal Control Problems

This paper presents an enhanced inertial Tseng’s extragradient method designed to address variational inequality problems involving pseudomonotone operators, along with fixed point problems governed by quasi-nonexpansive operators in real Hilbert spaces. Provided that the parameters satisfy appropriate conditions, the proposed method is shown to converge strongly. Finally, we provide computational results and illustrate their utility through optimal control applications. These aim to show the efficacy and superiority of the proposed algorithm compared with some existing algorithms.