On a general saddle-point condition in normed spaces

Abstract

The aim of this paper is two-fold. Firstly a theorem concerning necessary optimality conditions for problems in Euclidean spaces due to Rockafellar [ 1, Theorem 28.2] and proved by him by means of a rather special separation argument [1, Theorem 20.2] (involving several other theorems) is shown by means of an elementary separation argument. Secondly this theorem is generalized to normed spaces and is proven by means of an elementary corollary of the Hahn-Banach theorem.

DOI: 10.1007/BF01681334

Cite this paper

@article{Ponstein1975OnAG, title={On a general saddle-point condition in normed spaces}, author={Jacob Ponstein and Willem K. Klein Haneveld}, journal={Math. Program.}, year={1975}, volume={9}, pages={118-122} }