Nonsmooth Optimization

Manlio Gaudioso

ABSTRACT

We survey some of the most recognized proposals in the area of numerical methods for minimizing convex functions that are not necessarily differentiable. The approach is aimed at exposing the ideas at the basis of the methods, without discussing the complex technicalities that the interested reader may find in the extremely rich literature of the sector. We focus on the algorithms connected to the cutting-plane idea (bundle methods, methods of centers and the proximal point algorithm), on the finite min-max problem, and on some auxiliary problems relevant from a practical point of view.