Finite-time recurrent neural networks for solving nonlinear optimization problems and their application

This paper focuses on finite-time recurrent neural networks with continuous but non-smooth activation function solving nonlinearly constrained optimization problems. Firstly, definition of finite-time stability and finite-time convergence criteria are reviewed. Secondly, a finite-time recurrent neural network is proposed to solve the nonlinear optimization problem. It is shown that the proposed recurrent neural network is globally finite-time stable under the condition that the Hessian matrix of the associated Lagrangian function is positive definite. Its output converges to a minimum solution globally and finite-time, which means that the actual minimum solution can be derived in finite-time period. In addition, our recurrent neural network is applied to a hydrothermal scheduling problem. Compared with other methods, a lower consumption scheme can be derived in finite-time interval. At last, numerical simulations demonstrate the superiority and effectiveness of our proposed neural networks by solving nonlinear optimization problems with inequality constraints.