Inverse-free Dual Neural Networks for Online Solution of Strictly Convex Quadratic Programming

In view of its fundamental role arising in numerous fields of science and engineering, the problem of solving quadratic programs (QP) has been investigated extensively for the past decades. One of the state-of-the-art recurrent neural network (RNN) solvers/models is dual neural network (DNN). The dual neural network is of simple piecewise-linear dynamics and has global exponential convergence to optimal solutions. However, such a dual neural network was originally designed to solve quadratic programs with coefficient matrix W being positive-definite, entailing the inverse of IV. Considering that W could be nondiagonal and/or time-varying, two neural-network solvers are presented for the online computation of the inverse or its related term. By combining such matrix-inversion neural networks with the dual neural network, we could thus have inverse-free neural computation for solving online strictly-convex quadratic-programming problems. The effectiveness of the inverse-free dual-neural-network approach is further substantiated by computer-simulation results.