Acceptable Solutions and Backward Errors for Tensor Complementarity Problems

Shouqiang Du (), Weiyang Ding () and Yimin Wei ()
Additional contact information
Shouqiang Du: Qingdao University
Weiyang Ding: Fudan University
Yimin Wei: Fudan University

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 1, No 12, 260-276

Abstract: Abstract Backward error analysis reveals the numerical stability of algorithms and provides elaborate stopping criteria for iterative methods. Compared with numerical linear algebra problems, the backward error analysis for optimization problems is more rarely conducted in the literature. This paper is devoted to the backward error analysis for several generalizations of tensor complementarity problems. We first present sufficient and necessary conditions for the acceptable solutions for the extended tensor complementarity problem, the vertical tensor complementarity problem, and an extended form of tensor complementarity problem. Next, the backward errors for tensor complementarity problem are also proposed, which can be used to verify the stability of the tensor complementarity problem algorithms. Finally, some numerical examples are reported to illustrate the proposed backward errors for tensor complementarity problems.

Keywords: Acceptable solutions; Backward errors; Tensor complementarity problem; Extended tensor complementarity problem; Vertical tensor complementarity problem; 90C33; 15A69 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-020-01774-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:188:y:2021:i:1:d:10.1007_s10957-020-01774-y

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-020-01774-y

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().