An external penalty-type method for multicriteria∗

We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued method uses an auxiliary function, which can be chosen among large classes of “monotonic” real-valued mappings. We analyze the properties of the auxiliary functions in those classes and exhibit some examples. The convergence results are similar to those of the scalar-valued method and, depending on the kind of auxiliary function used in the implementation, under standard assumptions, the generated infeasible sequences converge to weak Pareto or Pareto optimal points. We also propose an implementable local version of the external penalization method and study its convergence results.