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.
