Expected residual minimization method for monotone stochastic tensor complementarity problem

Zhenyu Ming (), Liping Zhang () and Liqun Qi ()
Additional contact information
Zhenyu Ming: Tsinghua University
Liping Zhang: Tsinghua University
Liqun Qi: The Hong Kong Polytechnic University

Computational Optimization and Applications, 2020, vol. 77, issue 3, No 11, 896 pages

Abstract: Abstract In this paper, we first introduce a new class of structured tensors, named strictly positive semidefinite tensors, and show that a strictly positive semidefinite tensor is not an $$R_0$$ R 0 tensor. We focus on the stochastic tensor complementarity problem (STCP), where the expectation of the involved tensor is a strictly positive semidefinite tensor. We denote such an STCP as a monotone STCP. Based on three popular NCP functions, the min function, the Fischer–Burmeister (FB) function and the penalized FB function, as well as the special structure of the monotone STCP, we introduce three new NCP functions and establish the expected residual minimization (ERM) formulation of the monotone STCP. We show that the solution set of the ERM problem is nonempty and bounded if the solution set of the expected value (EV) formulation for such an STCP is nonempty and bounded. Moreover, an approximate regularized model is proposed to weaken the conditions for nonemptiness and boundedness of the solution set of the ERM problem in practice. Numerical results indicate that the performance of the ERM method is better than that of the EV method.

Keywords: Stochastic tensor complementarity problem; Strictly positive semidefinite tensor; Expected residual minimization; 90C33; 65K10 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-020-00222-x 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:coopap:v:77:y:2020:i:3:d:10.1007_s10589-020-00222-x

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-020-00222-x

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

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