TECHNICAL NOTE On the Characterization of Pareto-Optimal Solutions in Bicriterion Optimization

For bicriterion optimization involving objective functions fl and f2 defined on a decision space X, a condition is presented under which the Pareto-optimal points can be characterized as solutions of the scalar optimization problems: Minimize f~(x), subject to f2(x)<~a, x ~X, where a ranges over a certain interval. Using this condition, it is shown how the Pareto-optimat points can be so characterized in both convex and nonconvex situations.