Hongbo Sun – Optimization Online

A path-following framework on fiber bundle for variational inequalities

Published: 2026/05/30

Complementarity and Variational Inequalities fiber bundle, interior point method, path following, variational inequality

Variational inequality (VI) is a fundamental mathematical framework for many classical problems. We present a path-following framework for finite-dimensional VIs with arbitrary continuous functions and compact convex domains. The approach first approximately reduces a general VI to a smooth VI on simplex. Its key innovation is to formulate the smooth VI on simplex on a … Read more

A linearly convergent algorithm for variational inequalities based on fiber bundle

Published: 2025/09/27, Updated: 2026/06/02

Hongbo Sun

Complementarity and Variational Inequalities fiber bundle, interior point method, variational inequality problem

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