Contributed Session Fri.1.H 1029

Friday, 10:30 - 12:00 h, Room: H 1029

Cluster 15: Multi-objective optimization [...]

Bilevel optimization and risk management


Chair: Frank Heyde



Friday, 10:30 - 10:55 h, Room: H 1029, Talk 1

Johannes Jahn
GPU implementation of a multiobjective search algorithm

Coauthors: Dietmar Fey, Steffen Limmer


In this talk we discuss the use of graphics processing units (GPU) in multiobjective optimization. For a known multiobjective search algorithm with subdivision technique we describe a possible implementation and we present numerical results for test problems together with the achieved speed ups.



Friday, 11:00 - 11:25 h, Room: H 1029, Talk 2

Joerg Fliege
Reformulations of multiobjective bilevel problems

Coauthors: Konstantinos Kaparis, Huifu Xu


We present new approaches for multiobjective bilevel optimization, derived from an optimality condition for the lower level problem that leads naturally to a nonsmooth equality constraint. The nonsmoothness of the new constraint stems from its derivation as an optimal value function of a particular direction search problem. Preliminary numerical results on bilevel problems occuring in electricity markets show
the efficacy of the approach. Further, we consider possible extensions to the multilevel case.



Friday, 11:30 - 11:55 h, Room: H 1029, Talk 3

Frank Heyde
Set-valued average value at risk

Coauthors: Andreas Hamel, Birgit Rudloff, Benjamin Wei├čing


Since the seminal paper of Artzner, Delbaen, Eber and Heath
(1999), coherent measures of risk are considered to be an important tool for risk management. The most prominent example of a coherent risk measure is "Average (Conditional) Value at Risk (AVaR)''. In the presence of transaction costs it turned out that set-valued risk measures are in general better suited to cope with multiple markets than real-valued fuctions. A general theory of set valued convex risk measures was developed by Hamel, Heyde (2010) and Hamel, Heyde, Rudloff (2011). Within this framework we will present a set-valued version of the AVaR. A primal and dual description will be given which extend the real-valued case to the set-valued framework. The equivalence of the two descriptions is shown using a set-valued Fenchel-Rockafellar duality theorem developed by Hamel (2011).


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