Error Bounds of Regularized Gap Functions for Polynomial Variational Inequalities

This paper is devoted to presenting new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved polynomials. The main techniques are based on semialgebraic geometry and variational analysis, which allow us to establish a nonsmooth extension of the seminal Łojasiewicz gradient inequality to regularized gap functions with explicitly calculated exponents. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.