Neural network models for time-varying tensor complementarity problems

The existence and uniqueness of solutions and fast algorithms for tensor complementarity problems are hot topics in nowadays. We present a time-varying tensor complementarity problem (TVTCP) under tensor-tensor product (t-product). Theoretical analysis shows that the TVTCP is equivalent to a time-varying absolute value equation (TVAVE) under the mild conditions. Based on the absolute value equation, some neural networks for solving time-varying tensor inverse and TVTCP under the t-product are proposed and corresponding convergence are studied. Moreover, if the activation function (AF) of the neural networks is Mwsbp function, then we present the upper bound of the convergence time for the proposed neural networks. The numerical test results further illustrate that the proposed neural networks can solve time-varying tensor inverse and TVTCP effectively.