A recurrent neural network for real-time computation of semidefinite programming

This paper proposes a novel recurrent neural network for the real-time computation of semidefinite programming. This network is developed to minimize the duality gap between the admissible points of the primal problem and the corresponding dual problem. By appropriately defining an auxiliary cost function, a modified gradient dynamical system can be obtained which ensures an exponential convergence of the duality gap. Then, two subsystems are developed to avoid the difficulties involving matrix inverse and determinant, so that the resulted dynamical system can be easily realized using an analog recurrent neural network. The architecture of the resulting neural network is also discussed. The operating characteristics and performance of the proposed approach are demonstrated by means of simulation results. The approach reported in this paper not only gives a promising way for real-time computation of semidefinite programming, but also offers several new insights for its numerical computation