Lagrangian ANN for convex programming with linear constraints

Convex programming with linear constraints represents a large class of optimization problems which have wide applications, such as linear programming, quadratic programming and some network flow programming problems. In this paper we discuss the artificial neural network approach based on the Lagrangian multiplier method (Lagrangian ANN) to it. The emphases of the paper are on analysing the defect of premature of the conventional Lagrangian ANN and giving a new modification to it in order to overcome its premature defect. We prove that this modified Lagrangian ANN can always give the optimal solution. Numerical simulations demonstrate the effectiveness of the proposed modification.