Lecture Notes for IAP 2005 Course Introduction to Bundle Methods

Minimizing a convex function over a convex region is probably the core problem in the Nonlinear Programming literature. Under the assumption of the function of a differentiable function of interest, several methods have been proposed and successively studied. For example, the Steepest Descent Method consists of performing a line search along a descent direction given by minus the gradient of the function at the current iterate. One of the most remarkable applications of minimizing convex functions reveals itself within duality theory. Suppose we are interested in solving the following problem