Complementary Problems with Polynomial Data

Given polynomial maps \(f, g \colon \mathbb {R}^{n} \to {R}^{n}\), we consider the complementary problem of finding a vector \(x \in {R}^{n}\) such that $$ f(x) \ge 0, \quad g(x) \text{ and } \langle f(x), \rangle = 0. In this paper, present various properties on solution set problem, including genericity, nonemptiness, compactness, uniqueness as well error bounds with explicit exponents. These strengthen generalize some previously known results.