[This paper is concerned with the class of homogeneous programming problems. It is shown, to assure the existence of a saddlepoint for the associated Lagrangian, that some restrictions must be imposed on the degrees of homogeneity of the functions. Some properties of the perturbation function are also demonstrated.]

Gérald Leblanc, Paul van Moeseke; The Le Chatelier Principle in Convex Programming, The Review of Economic Studies, Volume 43, Issue 1, 1 February 1976, Pages 1