AUGMENTED LAGRANGIAN METHOD FOR SOLVING INEQUALITY CONSTRAINED NONLINEAR MIN-MAX OPTIMIZATION PROBLEMS

Abstract

In this project work nonlinear min-max optimization problems subject to inequality constraints were considered. The objective of this project work was to find an approximate solution of min-max optimization problems using the augmented Lagrangian method based on the KKT conditions. The method was implemented by updating the Lagrangian multiplier and by the value of penalty parameter, which is may also be adjusted iteratively. The convergence rate of the proposed method was done by using a limit of a norm for successive iteration and the error analysis of the method also was done by using a norm of consecutive iteration. The theoretical result of the min-max problem with the proposed method was numerically confirmed. Moreover, the efficiency and accuracy of the method illustrated by solving different test problems. As shown in the reported tables of examples, computing the convergence and error of the method. We obtained an approximate solution of min-max optimization problem by using the proposed method. Furthermore, the method could be easily performed by using MATLAB code.