Theorems of the Alternative for Inequality Systems of Real Polynomials

Sheng-Long Hu () and Zheng-Hai Huang ()
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Sheng-Long Hu: Tianjin University
Zheng-Hai Huang: Tianjin University

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 1, No 1, 16 pages

Abstract: Abstract In this paper, we establish theorems of the alternative for inequality systems of real polynomials. For the real quadratic inequality system, we present two new results on the matrix decomposition, by which we establish two theorems of the alternative for the inequality system of three quadratic polynomials under an assumption that at least one of the involved forms be negative semidefinite. We also extend a theorem of the alternative to the case with a regular cone. For the inequality system of higher degree real polynomials, defined by even order tensors, a theorem of the alternative for the inequality system of two higher degree polynomials is established under suitable assumptions. As a byproduct, we give an equivalence result between two statements involving two higher degree polynomials. Based on this result, we investigate the optimality condition of a class of polynomial optimization problems under suitable assumptions.

Keywords: Theorem of the alternative; Matrix decomposition; Polynomial system (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-012-9993-9

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