A neural network for solving nonlinear multilevel programming problems

This paper aims at utilizing the dynamic behavior of artificial neural networks to solve nonlinear multilevel programming (MLP) problems. Across complementarily slackness conditions base on entropic regularization, the optimization problem is converted into a system of nonlinear differential equations through use of an energy function and Lagrange multipliers. To solve the resulting differential equations, a steepest descent search technique is used. This proposed nontraditional algorithm is efficient for solving complex problems, and MLP problems can be solved on a real time basis. To illustrate the approach, several numerical examples are solved and compared.