Abstract
In this course we will study the relationship between vector
optimisation and polyhedral projection problems. Interestingly,
solving the (continuous) vector linear programme has deep connections
to the (discrete) problem of enumerating the vertices of a convex
polyhedron given its facet-defining inequalities (vertex enumeration
problem). One part of the course will introduce vector optimisation
according to the modern 'complete lattice' approach, another part will
cover required parts from the theory of convex polyhedra.
In the accompanying exercises we will also investigate software for
solving the problems studied in the lecture and conduct numerical
experiments.
Some prior knowledge about convex analysis would be helpful, but is
not strictly required.
Additional literature
Ehrgott, Matthias: Multicriteria optimization. 2005. 3-540-21398-8
Jahn, Johannes: Vector optimization - Theory, applications, and extensions. 2004. 3-540-20615-9
Ziegler, Günter M.: Lectures on polytopes. 1995. 0-387-94365-X
Grünbaum, Branko: Convex polytopes. 2003. 0-387-00424-6, 0-387-40409-0
Hamel, Andreas H. et al: Set optimization -- A rather short introduction. In: Set Optimization and Applications -- The State of the Art. From Relations to Set-valued Risk Measures. 2015. 978-3-662-48668-9, 978-3-662-48670-2 |
