PENALIZATION IN OPTIMIZATION OVER THE WEA KLY EFFICIENT SET

The paper deals with the problem of minimizing a scalar valued functio n over the weakly efficient (Pareto) set associated to a multicriteria minimization problem. This problem of post-Pareto analysis has severa l practical applications. Its main difficulty is due to the implicit f orm of the weakly efficient set and to the fact that, even in the line ar case, the problem is not convex. Mathematically this problem is cla ssified as a difficult global optimization problem. To solve it we use a penalty method. For the particular case of a linear vector problem and concave scalar objective, and also for the special case of linear functional, we propose an exact penalty algorithm which finds an optim al solution in a finite number of iterations.