Recurrent neural networks for solving linear inequalities and equations

This paper presents two types of recurrent neural networks, continuous-time and discrete-time ones, for solving linear inequality and equality systems . In addition to;the basic continuous-time and discrete-time neural-network models, two improved discrete-time neural networks with faster convergence rate are proposed by use of scaling techniques. The proposed neural networ ks can solve a linear inequality and equality system, can solve a linear pr ogram and its dual simultaneously, and thus extend and modify existing neur al networks for solving linear equations or inequalities, Rigorous proofs o n the global convergence of the proposed neural networks are given. Digital realization of the proposed recurrent neural networks are also discussed.