Optimization Letters

, Volume 13, Issue 2, pp 261–279 | Cite as

Stochastic \(R_0\) tensors to stochastic tensor complementarity problems

  • Maolin Che
  • Liqun Qi
  • Yimin WeiEmail author
Original Paper


The main purpose of this paper is devoted to an introduction of the stochastic tensor complementarity problem. We consider the expected residual minimization formulation of the stochastic tensor complementarity problem. We show that the solution set of the expected residual minimization problem is nonempty and bounded, if the associated tensor is an \(R_0\) tensor. We also prove that the associated tensor being a stochastic \(R_0\) tensor is a necessary and sufficient condition for the existence of the solution of the expected residual minimization problem to be nonempty and bounded.


Stochastic tensor complementarity problems Tensor complementarity problem \(R_0\) tensors Stochastic \(R_0\) tensors The expected residual minimization formulation 



The authors would like to thank the Editor-in-Chief Prof. Oleg Prokopyev, and two referees for their detailed comments and suggestions which greatly improve the presentation of our paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economic MathematicsSouthwest University of Finance and EconomicsChengduPeople’s Republic of China
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHung HomHong Kong
  3. 3.School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied MathematicsFudan UniversityShanghaiPeople’s Republic of China

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