Symbolic convex analysis

Convex optimization is a branch of mathematics dealing with non-linear optimization problems with additional geometric structure. This area has been the focus of considerable research due to the fact that convex optimization problems are scalable and can be efficiently solved by interior-point methods. Over the last ten years or so, convex optimization has found applications in many new areas including control theory, signal processing, communications and networks, circuit design, data analysis and finance. As with any new problem, of key concern is visualization of the problem space in order to develop intuition. In this thesis we develop tools for the visualization of convex functions. An important operation in convex optimization is that of Fenchel conjugation. Earlier research has developed algorithms for the symbolic Fenchel conjugation in one dimension, or many separable dimensions. In this thesis these algorithms are extended to work in the non-separable many dimensional case.