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    Numerische Mathematik und Optimierung

    SCHOOL: Winterschool 2018: Modern Methods in Nonsmooth Optimization [English]

    27.02.2018

    Nonsmooth optimization is a highly active field of research in the subject of applied and numerical mathematics. It requires sound knowledge of convex and nonsmooth analysis for the derivation and convergence analysis of modern methods to solve difficult and often nondifferentiable optimization problems. With Amir Beck (Israel), Christian Clason, Anton Schiela, Alexandra Schwartz (Germany) and Tuomo Valkonen (England) we were able to acquire five internationally renowned researchers as speakers. The lectures cover the range from theoretical foundations to the derivation and convergence analysis of optimization methods as well as their numerical realization and application. First, these topics will be explored for finite-dimensional optimization problems. Afterwards, the appropriate ideas and techniques will be transferred to infinite-dimensional problems.

    Speakers and Topics:

    • Amir Beck (Tel-Aviv University, Israel)
      First-Order Methods for Nonsmooth Optimization Problems

      Amir Beck is a world-leading expert for solution methods in nonsmooth optimization. He is well-known in particular for his contributions to the development of FISTA. He will give a lecture on first-order methods for nonsmooth optimization. The lecture will be algorithmically oriented by exploiting the special structure of several nonsmooth optimization problems and applications. Since this requires some knowledge from convex analysis, the necessary tools will also be presented.

    • Christian Clason (University of Duisburg-Essen, Germany)
      Introduction to Nonsmooth Infinite-Dimensional Optimization Problems

      Christian Clason is an expert for the solution of infinite-dimensional optimization problems using nonsmooth techniques. His lecture will present tools from nonsmooth analysis that can be used to derive necessary optimality conditions for infinite-dimensional optimization problems arising in optimal control, mathematical imaging, and inverse problems. A particular focus will be on optimality conditions in a form that is amenable to numerical solution.

    • Anton Schiela (University of Bayreuth, Germany)
      Optimization Methods in Function Space

      Anton Schiela is an expert for the solution of difficult infinite-dimensional optimization problems. The lecture will focus on algorithms for the solution of smooth and non-smooth optimization problems in a Banach or Hilbert space setting. Special emphasis will be put on the realization of such algorithms using proper discretization techniques.

    • Alexandra Schwartz (Technische Universität Darmstadt, Germany)
      Mathematical Programs with Complementarity Constraints and Related Problems

      Alexandra Schwartz is an expert for optimization problems with specially structured constraints. This includes mathematical programs with complementarity constraints or cardinality constraints. Her talks therefore focus on these topics. The necessary requirements from nonsmooth analysis will also be introduced within this lecture series.

    • Tuomo Valkonen (University of Liverpool, England)
      Preconditioned Proximal Point Methods in Hilbert Spaces

      Tuomo Valkonen is an expert for nonsmooth optimization methods and their applications to image reconstruction problems. The lecture will focus on modern iterative methods based on decoupling of the proximal point method. The necessary background from the field of variational analysis will also be provided.


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