Revisiting the Hahn–Banach theorem and nonlinear infinite programming

Abstract

The aim of this paper is to state a sharp version of the König supremum theorem, an equivalent reformulation of the Hahn–Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush–Kuhn–Tucker and Fritz John types, for nonlinear infinite programs. We also show that a weak concept of convexity coming from minimax theory, infsup-convexity, is the adequate one for this kind of results.