Several optimization methods have been developed for optimizing different kinds of optimization problems like linear and nonlinear, unconstrained and constrained etc. penalty function technique plays an important role in case of constrained optimization. The idea of this approach is to transform a constrained optimization problem to an unconstrained one by adding/subtracting a certain value to/from the objective function based on the amount of constraint violation occurred in a certain solution. There are two types of penalty function techniques, viz. the exterior and the interior methods. In case of exterior techniques, it is started with a feasible solution and then moved towards the feasible region. In the case of interior methods, the penalty term is chosen in such a way that its value will be small at the points away from the constraint boundaries and will tend to infinity as the constraint boundaries are approached. Thus, if we start from a feasible point, the subsequent points generated will always lie within the feasible region, since, the constraint boundaries act as the barriers during the optimization process. In this paper several penalty function techniques have been discussed so far available in the literature. Finally, some numerical examples have been given to illustrate the methods with the comparison also.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.