Global optimization based on TT-decomposition

In contrast to many other heuristic and stochastic methods, the global optimization based on TT-decomposition uses the structure of the optimized functional and hence allows one to obtain the global optimum in some problem faster and more reliable. The method is based on the TT-cross method of interpolation of tensors. In this case, the global optimum can be found in practice even in the case when the approximation of the tensor does not possess a high accuracy. We present a detailed description of the method and its justification for the matrix case and rank-1 approximation.

Finite-time boundedness for time-delay neural networks with external disturbances via weight learning approaches

This paper addresses the issue of finite-time boundedness for time-delay neural networks with external disturbances via weight learning. With the help of a group of inequalities and combining with the Lyapunov theory, weight learning rules are devised to ensure the neural networks to be finite-time bounded for the fixed connection weight matrix case and the fixed delayed connection weight matrix case, respectively. Sufficient conditions on the existence of the desired learning rules are presented in the form of linear matrix inequalities, which are easily verified by MATLAB software. It is shown that the proposed learning rules also guarantee the finite-time stability of the time-delay neural networks. Finally, a numerical example is employed to show the applicability of the devised weight learning rules.