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Characterization of solutions of multiobjective optimization problem. (English) Zbl 1072.90041
Weakly efficient points of (nonconvex) vector optimization problems are characterized as global optimal solutions of a constrained scalar optimization problem and vice versa. In this problem a convex, positively homogeneous and Lipschitzian function related to the distance function to the ordering cone is minimized over the set of values of the vector-valued objective function over the feasible set. Proper efficient solutions can then be characterized as global optimal solutions of the same problem with the additional property that this problem is Tykhonov well-posed. This result can then be used to find sufficient conditions for the equivalence of different notions of properly efficient points.
MSC:
90C30Nonlinear programming
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