Winter School 2018/2

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.

• Amir Beck (Tel-Aviv University, Israel)
  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)
  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)
  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.
• Alexandra Schwartz (Technische Universität Darmstadt, Germany)
  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)
  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.