Manoel Jardim – Optimization Online

Solving Quasi-Variational Inequalities Using the Progressive Decoupling of Linkages

Published: 2026/08/27

Complementarity and Variational Inequalities, Convex Optimization, Game Theory quasi-variational inequality; generalized Nash equilibrium problem; progressive decoupling; Spingarn’s partial inverse; proximal point method.

Inspired by the progressive decoupling of linkages methodology for optimization and variational inequalities, we propose an algorithm for solving quasi-variational inequalities as a sequence of variational inequalities. Our method is shown to converge locally under some regularity conditions and globally when such conditions hold throughout the entire domain. Separately, under other type of assumptions, global … Read more

A Dantzig-Wolfe Decomposition Method for Quasi-Variational Inequalities

Published: 2025/05/24, Updated: 2026/01/29

Complementarity and Variational Inequalities Quasi-variational inequality; Dantzig-Wolfe decomposition; Variational inequality; Walrasian equilibrium problem; Generalized Nash equilibrium problem.

We propose an algorithm to solve quasi-variational inequality problems, based on the Dantzig-Wolfe decomposition paradigm. Our approach solves in the subproblems variational inequalities, which is a simpler problem, while restricting quasi-variational inequalities in the master subproblems, making them generally much smaller in size when the original problem is large-scale. We prove global convergence of our … Read more