2024/10/29 by Vu Trung Hieu, Hieu, Vu Trung, Alfredo N. Iusem +5
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2410.21810
openalex publication_date 2024/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By using the squared slack variables technique, we demonstrate that the solution set of a general polynomial complementarity problem is the image, under a specific projection, of the set of real zeroes of a system of polynomials. This paper points out that, generically, this polynomial system has finitely many complex zeroes. In such a case, we use symbolic computation techniques to compute a univariate representation of the solution set. Consequently, univariate representations of special solutions, such as least-norm and sparse solutions, are obtained. After that, enumerating solutions boils down to solving problems governed by univariate polynomials. We also provide some experiments on small-scale problems with worst-case scenarios. At the end of the paper, we propose a method for computing approximate solutions to copositive polynomial complementarity problems that may have infinitely many solutions.