Newton-type methods for constrained optimization problems with PDEs

Prof. Dr. Michael Ulbrich

Abstract

This course develops Newton-type methods for inequality constrained optimization problems with PDEs. The main focus will be on semismooth Newton methods and their application to nonsmooth reformulations of the complementarity conditions or variational inequalites arising in the optimality systems. Over the past years, these methods have proven to be highly efficient and universally applicable. The approach allows for various extensions to, e.g., problems that involve nonsmooth terms in the objective function.

In the course, we plan to address the following topics:

  • optimality conditions
  • nonsmooth reformulation of optimality systems and variational inequalities
  • semismoothness and semismooth Newton methods in Banach spaces
  • semismooth superposition operators
  • regularization approaches for state constraints and related problems
  • globalization
  • mesh-independence
  • some numerical aspects (efficient solution of Newton systems etc.)
  • related Newton-type methods (interior point, ...)
  • various illustrations by model applications throughout the course
  • some extensions

Date and Place

  • 09.02.2015: 09:00 - 10:30, KFU SR 11.32
  • 09.02.2015: 10:45 - 12:15, KFU SR 11.32
  • 10.02.2015: 09:00 - 10:30, KFU SR 11.32
  • 10.02.2015: 10:45 - 12:15, KFU SR 11.32
  • 11.02.2015: 09:00 - 10:30, KFU SR 11.32
  • 11.02.2015: 10:45 - 12:15, KFU SR 11.32
  • 12.02.2015: 09:00 - 10:30, KFU SR 11.32
  • 12.02.2015: 10:45 - 12:15, KFU SR 11.32
  • 13.02.2015: 09:00 - 10:30, KFU SR 11.32
  • 13.02.2015: 10:45 - 12:15, KFU SR 11.32
 

TUM Mathematik Rutschen Universit√§t der Bundeswehr M√ľnchen Technische Universit√§t Graz Karl-Franzens-Universit√§t Graz Technische Universit√§t M√ľnchen
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