Invited Session Fri.3.H 0110

Friday, 15:15 - 16:45 h, Room: H 0110

Cluster 9: Global optimization [...]

Structural aspects of global optimization


Chair: Oliver Stein



Friday, 15:15 - 15:40 h, Room: H 0110, Talk 1

Georg Still
Minimization of nonconvex quadratic functions on special feasible sets


We are interested in global minimization of general quadratic functions
on a feasible set F. It is well-known that depending on the specific
set F the problem is possibly tractable or hard. We are especially interested in
the minimization on the unit simplex F. This problem is just the feasibility problem for copositive programming.
The latter recently attracted much attention as it appeared that
many hard integer problems can be represented exactly by copositive programs.
In our talk we firstly discuss some interesting properties
of quadratic functions such as the number of components of the level sets and the number of (global) minimizers.
We then consider copositive programming and give some
recent results on the structure of this problem.



Friday, 15:45 - 16:10 h, Room: H 0110, Talk 2

Tomas Bajbar
Nonsmooth versions of Sard's theorem


We present a comparison between some versions of Sard's Theorem which have been proven recently for special function classes with different definitions of critical points. The motivation for
calling a given point a critical point of a function varies. Considering the class of Ck functions, the
class of min-type functions or min-max functions, the motivation for the definition of critical point is
the topological structure of the inverse image. Considering the class of set-valued definable
mappings, the motivation for the definition of critical points is the property of metric regularity. We
compare topological critical points and critical points defined via metric regularity in the class of min-type
and min-max functions. We illustrate the whole problematic by some examples.



Friday, 16:15 - 16:40 h, Room: H 0110, Talk 3

Dominik Dorsch
Local models in equilibrium optimization

Coauthors: Hubertus Th. Jongen, Vladimir Shikhman


We study equilibrium optimization from a structural point of view. For that, we consider equilibrium optimization problems up to the smooth coordinate transformations locally at their solutions. The latter equivalence relation induces classes of equilibrium optimization problems. We focus on the stable classes corresponding to a dense set of data functions. We prove that these classes are unique and call them "basic classes''. Their representatives in the simplest form are called local models. For particular realizations of equilibrium optimization problems basic classes and their local models are elaborated. The latter include bilevel optimization, general semi-infinite programming and Nash optimization.


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