Exact Penalty Principle∗

Exact penalty approach aims at replacing a constrained optimization problem by an equivalent unconstrained optimization problem. Most of results in the literature of exact penalization are mainly concerned with finding conditions under which a solution of the constrained optimization problem is a solution of an unconstrained penalized optimization problem and the reverse property is rarely studied. In this paper we study the reverse property. We give conditions under which the original constrained (single and/or multiobjective) optimization problem and the unconstrained exact penalized problem are exactly equivalent. The main conditions to ensure the exact penalty principle for optimization problems include the global and local error bound conditions. By using variational analysis, these conditions may be characterized by using generalized differentiation.