The goal of this paper is to introduce and investigate a model called the stochastic tensor variational inequality(denoted by STVI),which is a natural extension of the stochastic linear complementarity problem and the...The goal of this paper is to introduce and investigate a model called the stochastic tensor variational inequality(denoted by STVI),which is a natural extension of the stochastic linear complementarity problem and the stochastic affine variational inequality.Firstly,the STVI is transformed into an expected residual minimization(ERM)problem involved the regularized gap function.Then,the properties of the ERM problem are investigated.Finally,a discrete approximation of ERM problem is obtained by quasi-Monte Carlo method.The convergence of optimal solutions and stationary points of the approximation problem are analyzed as well.展开更多
We discuss the uniqueness and the perturbation analysis for sparse non-negative tensor equations arriving from data sciences. By two different techniques, we may get better ranges of parameters to guarantee the unique...We discuss the uniqueness and the perturbation analysis for sparse non-negative tensor equations arriving from data sciences. By two different techniques, we may get better ranges of parameters to guarantee the uniqueness of the solution of the tensor equation. On the other hand, we present some perturbation bounds for the tensor equation. Numerical examples are given to show the efficiency of the theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(No.11961006)Guangxi Natural Science Foundation(No.2020GXNSFAA159100).
文摘The goal of this paper is to introduce and investigate a model called the stochastic tensor variational inequality(denoted by STVI),which is a natural extension of the stochastic linear complementarity problem and the stochastic affine variational inequality.Firstly,the STVI is transformed into an expected residual minimization(ERM)problem involved the regularized gap function.Then,the properties of the ERM problem are investigated.Finally,a discrete approximation of ERM problem is obtained by quasi-Monte Carlo method.The convergence of optimal solutions and stationary points of the approximation problem are analyzed as well.
基金The authors would like to thank the referees for their helpful comments. The first author was supported by the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University （Grant No. 2018008） the second author was supported by the National Natural Science Foundation of China （Grant Nos. 11671185, 11771159）, and Major Project （Grant No. 2016KZDXM025）, and Innovation Team Project （Grant No. 2015KCXTD007） of Guangdong Provincial Universities+1 种基金 the third author was supported in part by HKBGC GRF 1202715, 12306616, 12200317 and HKBU RC-ICRS/16-17/03 the fourth author was supported by University of Macao （Grant No. MYRG2017-00098-FST） and the Macao Science and Technology Development Fund （050/2017/A）.
文摘We discuss the uniqueness and the perturbation analysis for sparse non-negative tensor equations arriving from data sciences. By two different techniques, we may get better ranges of parameters to guarantee the uniqueness of the solution of the tensor equation. On the other hand, we present some perturbation bounds for the tensor equation. Numerical examples are given to show the efficiency of the theoretical results.
