A Comprehensive Study on Nonlinear Variational Inequalities in Convex Optimization

Abstract

This study investigates nonlinear variational inequalities (NVIs) has a core model in convex optimization (CO) and evaluates their theoretical and numerical relevance. The paper works through, NVIs in terms of formulation and properties of their solutions. Steady-state and time-dependent cases are addressed through projection methods and augmented Lagrangian methods to show their performance in solving optimization problems. The work presented here shows the usefulness of NVIs through practical examples in traffic equilibrium, in economic modeling, and in engineering optimization. Numerical experiments with the developed algorithms and detailed graphical results reveal the factors affecting convergence, the efficiency of NVIs and their applicability to solve various optimization problems.