11h30 - 11h55
Convergence of a Scholtes-Type Relaxation Method for Optimization Problems with Cardinality Constraints
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.
11h55 - 12h20
Convex analysis of the generalized matrix-fractional function
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.
12h20 - 12h45
Stability of minimizers of set optimization problems
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.