Computing Stationary Points of Bilevel Problems with a Penalty Alternating Direction Method

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Details zur Publikation

Autor(en): Kleinert T, Schmidt M
Jahr der Veröffentlichung: 2019
Sprache: Englisch


Abstract

Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, etc. Often, these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization one develops primal heuristics in order to obtain feasible points of good quality quickly or to enhance the search process of exact global methods. However, there are comparably few heuristics for bilevel problems. In this paper we develop such a primal heuristic for bilevel problems with mixed-integer linear or quadratic upper level and linear or quadratic lower level. The heuristic is based on a penalty alternating direction method, which also allows for a theoretical analysis. We derive a convergence theory stating that the method converges to a stationary point of an equivalent single-level reformulation of the bilevel problem. Finally, we extensively test the method on a large instance set and illustrate its good performance both in terms of running times and solution quality.


FAU-Autoren / FAU-Herausgeber

Kleinert, Thomas
Juniorprofessur für Optimierung von Energiesystemen
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen


Zitierweisen

APA:
Kleinert, T., & Schmidt, M. (2019). Computing Stationary Points of Bilevel Problems with a Penalty Alternating Direction Method.

MLA:
Kleinert, Thomas, and Martin Schmidt. Computing Stationary Points of Bilevel Problems with a Penalty Alternating Direction Method. 2019.

BibTeX: 

Zuletzt aktualisiert 2019-23-04 um 15:18