Symbolic Fenchel Conjugation

Of key importance in convex analysis and optimization is the notion of duality, and in particular that of Fenchel duality. This work explores improvements to existing algorithms for the symbolic calculation of subdifferentials and Fenchel conjugates of convex functions defined on the real line. More importantly, these algorithms are extended to enable the symbolic calculation of Fenchel conjugates on a class of real-valued functions defined on $\mathbb{R}^n$ . These algorithms are realized in the form of the Maple package SCAT.