In this paper, we introduce several classes of generalized convex functions already discussed in the literature and show the relation between these classes. Moreover, a Gordan–Farkas type theorem is proved for all these classes and it is shown how these theorems can be used to verify strong Lagrangian duality results in finite-dimensional optimization.

Gordan–Farkas type theorems, Lagrangian duality, generalized convexity,
Journal of Optimization Theory and Applications
Erasmus School of Economics

Frenk, J.B.G, & Kassay, G. (1999). On Classes of Generalized Convex Functions, Gordan–Farkas Type Theorems, and Lagrangian Duality. Journal of Optimization Theory and Applications, 102, 315–343. doi:1021780423989