Comparison of Some Penalty and Barrier Techniques in Direct Search Methods

Constrained nonlinear optimization problems are very common in real live situations and in several areas of knowledge. To handle the constrains in these problems Penalty and barrier techniques are widely used. In penalty or barrier methods a sequence of unconstrained problems is constructed and then they are solved using unconstrained optimization methods. These methods attempt to minimize simultaneously both the objective and the constraint violation functions, defining a sequence of new objective functions which include information about the objective function and these violations. There are some real life scenarios where the derivatives are not know or are not accessible, because the involved functions are non smooth, non continuous, non convex and/or with many local minima. Therefore in such problems unconstrained optimization direct search methods must be used. This work presents a comparison of some penalty and barrier techniques in direct search methods.