Notes on the Optimization Problems Corresponding to Polynomial Complementarity Problems

Vu Trung Hieu (), Yimin Wei () and Jen-Chih Yao ()
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Vu Trung Hieu: Phuong Dong University
Yimin Wei: Fudan University
Jen-Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 2, No 19, 687-695

Abstract: Abstract This work is motivated by a conjecture of Che et al. (J Optim Theory Appl 168:475–487, 2016) which says that if the feasible region of a tensor complementarity problem is nonempty, then the corresponding optimization problem has a solution. The aim of the paper is twofold. First, we show several sufficient conditions for the solution existence of the optimization problems corresponding to polynomial complementarity problems. Consequently, some results for tensor complementarity problems are obtained. Second, we disprove the conjecture by giving a counterexample.

Keywords: Polynomial complementarity problem; Tensor complementarity problem; Polynomial optimization problem; Feasible region; Solution existence; 90C33; 11C08 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-019-01596-7

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