On the LVI-based primal-dual neural network for solving online linear and quadratic programming problems

Motivated by real-time solution to robotic problems, researchers have to consider the general unified formulation of linear and quadratic programs subject to equality, inequality and bound constraints simultaneously. A primal-dual neural network is presented in this paper for the online solution based on linear variational inequalities (LVI). The neural network is of simple piecewise-linear dynamics, globally convergent to optimal solutions, and able to handle linear and quadratic problems in the same manner. Other robotics-related properties of the LVI-based primal-dual network are also investigated, like, the convergence starting within feasible regions, and the case of no solutions.