fiber bundle

The fixed-point bundle method over product-of-simplex domains arising from game equilibria

Categories Complementarity and Variational Inequalities, Game Theory Tags , , , ,

Developing general-purpose algorithms with global asymptotic convergence guarantees for Nash equilibria of general-sum games remains a longstanding challenge. This paper extends the fixed-point bundle framework for finite-dimensional variational inequalities (VIs) from simplex domains to product-of-simplex domains, enabling its direct application to Nash equilibrium computation. The resulting fixed-point bundle exhibits a composite fiber bundle structure. The … Read more

A path-following framework on fiber bundle for variational inequalities

Categories Complementarity and Variational Inequalities Tags , , ,

Developing general-purpose algorithms with global asymptotic convergence guarantees for variational inequalities (VIs) remains a longstanding challenge. This paper proposes a path-following framework for finite-dimensional VIs with arbitrary continuous mappings and polytope domains. The approach first transforms a general VI into a smooth VI on a simplex. Its key innovation is to formulate the resulting problem … Read more

A linearly convergent algorithm for variational inequalities based on fiber bundle

Categories Complementarity and Variational Inequalities Tags , ,

The variational inequality (VI) problem is a fundamental mathematical framework for many classical problems. This paper introduces an algorithm that applies to arbitrary finite-dimensional VIs with general compact convex sets and general continuous functions. The algorithm guarantees global linear convergence to an approximate solution without requiring any assumptions, including the typical monotonicity. Our approach adapts … Read more