3 Presentations

• 
  11:30 AM - 11:55 AM

  Convergence of a Scholtes-Type Relaxation Method for Optimization Problems with Cardinality Constraints

  • Alexandra Schwartz, presenter, TU Darmstadt
  • Martin Branda, Charles University Prague
  • Max Bucher, TU Darmstadt
  • Michal Cervinka, Charles University, Prague

  Optimization problems with cardinality constraints have applications for example in portfolio optimization. However, due to the discrete-valued cardinality constraint, they are not easy to solve. We provide a continuous reformulation of cardinality constraints and discuss the convergence of a Scholtes-type relaxation method for the resulting nonlinear programs with orthogonality constraints. Furthermore, we show preliminary numerical results for portfolio optimization problems with different risk measures.

• 
  11:55 AM - 12:20 PM

  Convex analysis of the generalized matrix-fractional function

  • Tim Hoheisel, presenter, McGill University

  We study the support functional of a graph of a matrix-valued mapping intersected with an affine manifold. This support function establishes a connection between optimal value functions for quadratic optimization problems, the matrix-fractional function, the pseudo matrix-fractional function, the nuclear norm, and multi-task learning. As a core result we present a new and elegant description of the closed convex hull of the supported set which opens the door for various applications, many of which will be presented in the talk.

• 
  12:20 PM - 12:45 PM

  Stability of minimizers of set optimization problems

  • Michel GEOFFROY, presenter, Université des Antilles (LAMIA)

  We investigate, in a unified way, the stability of several relaxed minimizers of set optimization problems.
  To this end, we introduce a topology on vector ordered spaces from which we derive a concept of convergence that allows us to study both the upper and the lower stability of the sets of relaxed minimizers we consider.