Complementary problems with polynomial data

2019/08/01 by Tien-Son Pham, Pham, Tien-Son, Canh Hung Nguyen +1
Mathematics · #90C33 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:90C33

paper · pdf · doi:10.48550/arxiv.1908.00332

arxiv created 2019/08/01 · arxiv updated 2019/08/02

Abstract

Given polynomial maps f, g \colon ℝⁿ → ℝⁿ, we consider the \em polynomial complementary problem of finding a vector x ∈ ℝⁿ such that f(x) ≥ 0, g(x) ≥ 0, \textrm and ⟨ f(x), g(x) ⟩ = 0. 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.

Related

• Polynomial complementarity problems
• Univariate representations of solutions to generic polynomial complementarity problems
• Using vector divisions in solving linear complementarity problem
• Properties of the solution set of generalized polynomial complementarity problems
• Solution maps of polynomial variational inequalities