- Complementary problems with polynomial data Tien-Son PHAM(sonptdlu.edu.vn) Canh Hung NGUYEN(hungncntu.edu.vn) Abstract: Given polynomial maps $f, g \colon \mathbb{R}^n \to \mathbb{R}^n,$ we consider the {\em polynomial complementary problem} of finding a vector $x \in \mathbb{R}^n$ such that \begin{equation*} f(x) \ \ge \ 0, \quad g(x) \ \ge \ 0, \quad \textrm{ and } \quad \langle f(x), g(x) \rangle \ = \ 0. \end{equation*} In this paper, we present various properties on the solution set of the problem, including genericity, nonemptiness, compactness, uniqueness as well as error bounds with exponents explicitly determined. These strengthen and generalize some previously known results, and hence broaden the boundary knowledge of nonlinear complementarity problems as well. Keywords: Polynomial complementarity problem, Existence, Boundedness, Uniqueness, Error bound, Genericity Category 1: Complementarity and Variational Inequalities Citation: Download: [PDF]Entry Submitted: 08/17/2019Entry Accepted: 08/17/2019Entry Last Modified: 08/17/2019Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.