This paper extends the fixed-point bundle framework for finite-dimensional variational inequalities (VIs) from the simplex domain to the product-of-simplex domain, which is directly applicable to solving Nash equilibria. The fixed-point bundle for VIs on the product-of-simplex domain reveals a composite fiber bundle structure. The key innovation is to construct an equivalent VI on the simplex … Read more
This paper proposes a path-following framework for finite-dimensional variational inequalities with arbitrary continuous functions and compact convex domains. The approach first approximately reduces a general variational inequality to a smooth variational inequality on a simplex. Its key innovation is to formulate the smooth variational inequality on a simplex on a fiber bundle called the fixed-point … Read more
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