ABSTRACT

Convex functions play a vital role in almost all the branches of mathematics as well as other areas such as science, economics, and engineering. The main reason for this being that they are very well suited to extremum problems as necessary conditions for the existence of a minimum also become sufficient in the presence of convexity. Convex functions were introduced in the beginning of the 20th century by Jensen [111] and more than forty years later a thorough study of conjugate functions was initiated by Fenchel [76, 77]. The lecture notes by Fenchel [77] led to the classic book Convex Analysis by Rockafellar [182].