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Bilevel Optimization: on the Structure of the Feasible Set

We consider bilevel optimization from the optimistic point of view. Let the pair (x,y) denote the variables. The main difficulty in studying such problems lies in the fact that the lower level contains a global constraint. In fact, a point (x,y) is feasible if y solves a parametric optimization problem L(x). In this paper we restrict ourselves to the special case that the variable x is one-dimensional. We describe the generic structure of the feasible set M. Moreover, we discuss local reductions of the bilevel problem as well as corresponding optimality criteria. Finally, we point out typical problems that appear when trying to extend the ideas to higher dimensional x-dimensions. This will clarify the high intrinsic complexity of the general generic structure of the feasible set M and corresponding optimality conditions for the bilevel problem U. In collaboration with H. Th. Jongen.
Type of Seminar:
Optimization and Applications Seminar
Dipl.-Math. Vladimir Shikhman
RWTH Aachen, Germany
Sep 27, 2010   16:30-18:00

ETHZ Rämistrasse 101, HG G 19.1
Contact Person:

Prof. John Lygeros
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