Stochastic structured tensors to stochastic complementarity problems

This paper is concerned with the stochastic structured tensors to stochastic complementarity problems. The definitions and properties of stochastic structured tensors, such as the stochastic strong P-tensors, stochastic P-tensors, stochastic \(P_{0}\)-tensors, stochastic strictly semi-positive tensors and stochastic S-tensors are given. It is shown that the expected residual minimization formulation (ERM) of the stochastic structured tensor complementarity problem has a nonempty and bounded solution set. Interestingly, we partially answer the open questions proposed by Che et al. (Optim Lett 13:261–279, 2019). We also consider the expected value method of stochastic structured tensor complementarity problem with finitely many elements probability space. Finally, based on the expected residual minimization formulation (ERM) of the stochastic structured tensor complementarity problem, a projected gradient method is proposed for solving the stochastic structured tensor complementarity problem and the related numerical results are also given to show the efficiency of the proposed method.