In this paper an intuitive and geometric approach is presented explaining the basic ideas of convex/quasiconvex analysis and its relation to duality theory. As such, this paper does not contain new results but serves as a hopefully easy introduction to the most important results in duality theory for convex/quasiconvex functions on locally convex real topological vector spaces. Moreover, its connection to optimization is also discussed.

dual problem, duality theory, perturbation function, convex case, quasiconvex function,
Lecture Notes in Economics and Mathematical Systems
Erasmus School of Economics

Frenk, J.B.G, Dias, D.M.L, & Gromicho, J.A.S. (1994). Duality theory for convex/quasiconvex functions and its application to optimization. In Generalized Convexity. Lecture Notes in Economics and Mathematical Systems. (pp. 153–170). doi:10.1007/978-3-642-46802-5_14