Generalized Polynomial Complementarity Problems over a Polyhedral Cone

Tong-tong Shang (), Jing Yang and Guo-ji Tang ()
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Tong-tong Shang: Guangxi University for Nationalities
Jing Yang: Guangxi University for Nationalities
Guo-ji Tang: Guangxi University for Nationalities

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 2, No 3, 443-483

Abstract: Abstract The goal of this paper is to investigate a new model, called generalized polynomial complementarity problems over a polyhedral cone and denoted by GPCPs, which is a natural extension of the polynomial complementarity problems and generalized tensor complementarity problems. Firstly, the properties of the set of all $$R^{K}_{{\varvec{0}}}$$ R 0 K -tensors are investigated. Then, the nonemptiness and compactness of the solution set of GPCPs are proved, when the involved tensor in the leading term of the polynomial is an $$ER^{K}$$ E R K -tensor. Subsequently, under fairly mild assumptions, lower bounds of solution set via an equivalent form are obtained. Finally, a local error bound of the considered problem is derived. The results presented in this paper generalize and improve the corresponding those in the recent literature.

Keywords: Generalized polynomial complementarity problem; Polyhedral cone; $$R^{K}_{{\varvec{0}}}$$ R 0 K -tensor; Existence; Lower bound; Error bound; 90C33; 90C23; 14P10; 54C60 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-021-01969-x

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