Existence of Solutions of Mixed Variational-like Inequalities and Gap Functions - Ram, Tirth; Bhagat, Zeenat (Communications in Mathematics and Applications, 2024)
In this work, a gap function and an extended gap function are introduced, which gives rise to an optimization problem formulation to  mixed variational-like inequalities. Furthermore, a convex lower bound to an extended gap function for Stampachhia and Minty mixed variational-like inequality problems is developed. The results presented in this paper generalize some well-known results of several authors, which play a significant role in the theory of variational inequalities.
Keywords: Gap function; Pseudomonotonicity; Strongly monotone; Lipschitz continuous