### V5E1-Advanced Topics in Numerical Methods in Science and Technology
(Winter Term 2016/17)

## Nonsmooth Analysis and Optimization

Nonsmooth optimization is devoted to the general problem of minimizing functions that are
typically not differentiable at their minimizers. In order to optimize nonsmooth functions, the classical theory of optimization cannot be directly used due to lacking
certain differentiability and strong regularity conditions. However, because of the complexity of the real world, functions used in practical
applications are often nonsmooth. Nonsmooth problems appear in many fields of applications, for example
in image denoising, optimal control, neural network training, data mining, economics and computational
chemistry and physics, therefore it is of eminent importance to be able to optimize a nonsmooth function.
This course aims to provide a basic working understanding of nonsmooth analysis
and its applications in optimization. Intended topics include:

- Nonsmooth differential theory
- Tangent and Normal cones
- Nonsmooth optimization theory
- Bundle methods
- Quasi-newton methods

Recommended literature:

- Marko. M. Mäkelä, Pekka. Neittaanmäki, Nonsmooth Optimization; Analysis and Algorithms with Applications to Optimal Control, World Scientific, 1992.
- Frank H. Clarke, Optimization and Nonsmooth Analysis, Society for Industrial and Applied
Mathematics, 1990.
- Boris. S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory,
Grundlehren Series, 331, Springer, New York (2006).
- F. H. Clarke, Yu. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control
Theory, Graduate Texts in Mathematics 178, Springer, New York (1998).

Prerequisites: analysis and linear algebra (Bachelor level), smooth optimization methods (Steepest descent methods, Newton methods etc.).

Date & time: | Tuesday and Thursday | 14:15–15:45 Uhr, | Wegelerstr. 6, Room 6.020 |

Begin: | Tuesday, | 18.10.2016 |