On the Simplified LVI-based Primal-Dual Neural Network for Solving LP and QP Problems

Motivated by real-time solution to robotic issues, researchers have considered the general unified problem-formulation of linear programs (LP) and quadratic programs (QP) subject to equality, inequality and bound constraints simultaneously (Y. Zhang, 2002), (Y. Zhang, 2005). An LVI-based primal-dual neural network (LVI-PDNN) has been developed for such an online solution (Y. Zhang, 2005). It is with simple piecewise-linear dynamics, global convergence to optimal solutions, and ability to handle linear-programs and quadratic-programs in real time and in the same manner. In this paper, to further reduce the implementation and computational complexities, a simplified LVI-PDNN model (T.L. Friesz et al., 1994) is investigated. Interesting numerical results and properties of this simplified LVI-based primal-dual neural network are discussed. For example, the convergence starting within feasible region, the case of no solutions, and the oscillation in solving LP problems.