A recurrent neural network for real-time semidefinite programming

The semidefinite programming problem is an important optimization problem that has been extensively investigated. A real-time solution method for solving such a problem, however, is still not yet available. The paper proposes a recurrent neural network for this purpose. First, an auxiliary cost function is introduced to minimize the duality gap between the admissible points of the primal problem and the corresponding dual problem. Then a dynamical system is constructed to drive the duality gap to zero exponentially along any trajectory by modifying the gradient of the auxiliary cost function. Furthermore, a subsystem is developed to circumvent the computation of matrix inverse, so that the resulting overall dynamical system can be realized using a recurrent neural network. The architecture of the resulting neural network is discussed. The operating characteristics and performance of the proposed approach are demonstrated by means of simulation results