Verallgemeinert konvexe vektorfunktionen und der anwendung in der vektoroptimierung
- 1 January 1979
- journal article
- research article
- Published by Taylor & Francis in Mathematische Operationsforschung und Statistik. Series Optimization
- Vol. 10 (3), 303-316
- https://doi.org/10.1080/02331937908842581
Abstract
Generalized convexity properties of vector functions in Rn /Rm with respect to a convex cone are studied. It is shown that the well-known connections between the various kinds of convexity, quasi-and pseudoconvexity of functionals can be extended to vector functions only to a part. The study of convexity properties with respect to convex polyhedral cones yields correspondences between the properties of vector functions and their components, respectively linear combinations of their components. As an example for the application of generalized convex vector functions a vector optimization problem with semi orderings defined by convex cones is considered. Besides a necessary and sufficient condition for the convexity of the feasible set, sufficient optimality conditions of Kuhn-Tucker and Fritz-John type are given.Keywords
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