The influence of proper efficiency on optimal solutions of scalarizing problems in multicriteria optimization

The paper investigates scalarizations for the determination of Pareto optima of multicriteria optimization problems which deliver properly efficient points in the sense of Geoffrion. Proper efficiency in the sense of Schönfeld is generalized by the simultaneous consideration of several weighted sums of the objective functions. This problem is geometrically interpreted by means of a polyhedral cone. This specialization of the parameters induces an extension of the weighted Chebyshev norm minimization for which the paper proves conditions for the existence of optimal solutions and statements confirming known more special results.