On error bounds of polynomial complementarity problems with structured tensors. (1st February 2018)

• Record Type: Journal Article
• Authors: Ling, Liyun; He, Hongjin; Ling, Chen
• Is Part Of: Optimization. Volume 67:Number 2(2018)
• Page Start: 341
• Page End: 358
• Publication Date: 2018-02-01
• Subjects: Error bound -- polynomial complementarity problem -- semicopositive function -- P-function -- ER-tensor; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1391254
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: The recently introduced polynomial complementarity problem (PCP) is an interesting generalization of the tensor complementarity problem (TCP) studied extensively in the literature. In this paper, we make a contribution to analysing the error bounds of PCPs with structured tensors. Specifically, we first show that the solution set of PCPs with a leadingER -tensor is nonempty and compact. Then, we analyse lower bounds of solutions of PCPs under the strict semicopositiveness, thereby gainfully establishing error bounds of PCPs, which, to the best of our knowledge, are not studied in the current PCPs and TCPs literature. Moreover, it is noteworthy that, due to the special structure of PCPs, our error bounds are better than the direct results obtained by applying the theory of non-linear complementarity problems to PCPs.