Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraints

Extended linear-quadratic programming (ELQP) is an extension of the conventional linear programming and quadratic programming, which arises in many dynamic and stochastic optimization problems. Existing neural network approaches are limited to solve ELQP problems with bound constraints only. In the paper, I consider solving the ELQP problems with general polyhedral sets by using recurrent neural networks. An existing neural network in the literature, called general projection neural network (GPNN) is investigated for this purpose. In addition, based on different types of constraints, different approaches are utilized to lower the dimensions of the designed GPNNs and consequently reduce their structural complexities. All designed GPNNs are stable in the Lyapunov sense and globally convergent to the solutions of the ELQP problems under mild conditions. Numerical simulations are provided to validate the results.