ALOP-Colloquium with Prof. Dr. Steven Gabriel, University of Maryland

On Monday, January 25, 2021 at 16:00 c.t. Prof. Dr. Steven Gabriel of the University of Maryland , Baltimore will present his recent work at our colloquium entitled

A parametric programming approach to bilevel optimisation with lower-level variables in the upper level

This paper examines linearly constrained bilevel programming problems in which the upper-level
objective function depends on both the lower-level primal and dual optimal solutions. We parametrize
the lower-level solutions and thereby the upper-level objective function by the upper-level variables
and argue that it may be non-convex and even discontinuous. However, when the upper-level
objective is affine in the lower-level primal optimal solution, the parametric function is piece-wise linear.
We show how this property facilitates the application of parametric programming and demonstrate how
the approach allows for decomposition of a separable lower-level problem. When the upper-level
objective is bilinear in the lower-level primal and dual optimal solutions, we also provide an exact
linearisation method that reduces the bilevel problem to a single-level mixed-integer linear programme
(MILP). We assess the performance of the parametric programming approach on two case studies of
strategic investment in electricity markets and benchmark against state-of-the-art MILP and non-linear
solution methods for bilevel optimisation problems. Preliminary results indicate substantial
computational advantages over several standard solvers, especially when the lower-level problem
separates into a large number of subproblems. Furthermore, we show that the parametric
programming approach succeeds in solving problems to global optimality for which standard methods
can fail.

For further information, please refer to this article: Henrik C. Bylling, Steven A. Gabriel & Trine K. Boomsma (2020) A parametric programming approach to bilevel optimisation with lower-level variables in the upper level, Journal of the Operational Research Society, 71:5, 846-865, DOI: 10.1080/01605682.2019.1590132
To link to this article: https://doi.org/10.1080/01605682.2019.1590132

This presentation will take place via ZOOM. A link will be e-mailed prior to the event.