A Novel Method for Solving Equality and Inequality Constrained Nonlinear Optimization Problems with Artificial Neural Networks

Abstract

In this research, we study how artificial neural network can be used in solving both equality and inequality constrained non-linear optimization problems. The procedure involves generating a system of differential equations which must correspond to the given number of intrinsic variables. We proceed to apply this technique to solve some constrained non-linear optimization problems. Using MathCAD14, we were able to generate the corresponding system of differential equations developed using the neural network gradient scheme. We provide the resulting graphical profiles of the solutions and compared it with the analytic solution. Our steps and results indicate that, for the problems tested, the neural network approach can be more straightforward to implement and avoids some of the iterative assumptions of classical methods.