fiber bundle – Optimization Online

A path-following framework on fiber bundle for variational inequalities

Published: 2026/05/30, Updated: 2026/06/30

Hongbo Sun

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

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

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