Solution Sets of Quadratic Complementarity Problems

Jie Wang (), Shenglong Hu () and Zheng-Hai Huang ()
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Jie Wang: Tianjin University
Shenglong Hu: Tianjin University
Zheng-Hai Huang: Tianjin University

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 1, No 7, 120-136

Abstract: Abstract In this paper, we study quadratic complementarity problems, which form a subclass of nonlinear complementarity problems with the nonlinear functions being quadratic polynomial mappings. Quadratic complementarity problems serve as an important bridge linking linear complementarity problems and nonlinear complementarity problems. Various properties on the solution set for a quadratic complementarity problem, including existence, compactness and uniqueness, are studied. Several results are established from assumptions given in terms of the comprising matrices of the underlying tensor, henceforth easily checkable. Examples are given to demonstrate that the results improve or generalize the corresponding quadratic complementarity problem counterparts of the well-known nonlinear complementarity problem theory and broaden the boundary knowledge of nonlinear complementarity problems as well.

Keywords: Quadratic complementarity problem; Tensor; Copositivity; Uniqueness; 90C33; 15A69; 49N60 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-017-1205-1

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