NUMERICAL TREATMENT FOR CONSTRAINED OPTIMIZATION PROBlEMS AND ITS APPUCAnON IN OPTIMAlCONTROPl ROBlEMS .

Abstract

Our objective "of this thesis, which consists of five chapters, is to introduce a new numerical methods for solving constrained optimization problems by using the approach of Exponential-Penalty function with the partial quadratic interpolation (EPPQI) method in the unconstrained optimization problems (El-Gindy 1977). Also we use these methods to solve both linear and non-linear optimal control problems using our proposed method.

In chapter one, we give a classification and survey of some known methods for solving unconstrained and constrained optimization problems, and a survey of some known methods for solving the optimal control problems. Also we introduce in some details, the partial quadratic interpolation technique in the constrained optimization problems (El-Gindy 1977).

In chapter two, we present a new method for solving constrained optimization problems. The method based on the approach of the Exponential-Penalty function with the partial • quadratic interpolation (EPPQI) method in unconstrained optimization problems.