Bilevel Optimization
Mathematical models in which one optimization problem is constrained by the solution of another.
Research
I work in mathematical optimization at Trier University, where I am Professor of Nonlinear Optimization. Bilevel optimization is a central focus of my research, alongside mixed-integer and nonlinear methods, optimization under uncertainty, equilibrium and game-theoretic problems, and network optimization.
Core Research Topics
Mixed-Integer & Nonlinear Optimization
Theory and algorithms for optimization problems that combine discrete decisions with nonlinear constraints and objectives.
Robust Optimization & Uncertainty
Models and algorithms for optimization under uncertain parameters, including robust and decision-dependent formulations.
Equilibrium Problems & Games
Models and algorithms for interacting decision-makers, complementarity systems, and generalized Nash equilibrium problems.
Network Optimization
Optimization models and algorithms for flows and decisions on energy and infrastructure networks.
Selected Research
A curated cross-section of publications and open research resources.
Benchmark Library
BOBILib
An open library of bilevel optimization benchmark instances in a standardized format.
BOBILib websiteBook
Linear and Mixed-Integer Bilevel Optimization: Theory and Algorithms
Yasmine Beck, Ivana Ljubić, Martin Schmidt
View publicationJournal Article
A survey on bilevel optimization under uncertainty
Yasmine Beck, Ivana Ljubić, Martin Schmidt
View publicationJournal Article
Adjustable robust nonlinear network design without controllable elements under load scenario uncertainties
Johannes Thürauf, Julia Grübel, Martin Schmidt
View publicationCurrent Projects
SymBi
SymBi: Exploiting Symmetries for Faster Bilevel Optimization Algorithms
Development of mathematical theory and algorithms for detecting and exploiting symmetries in bilevel optimization problems.
- Funding
- German Research Foundation (DFG) and Dutch Research Council (NWO)
- Partners
- Eindhoven University of Technology (Christopher Hojny)
A3G
A3G: Aggregative gemischt-ganzzahlige Gleichgewichtsprobleme: Existenz, Approximation und Algorithmen
Study of the existence, approximation, and computation of equilibria in aggregative games with discrete strategy spaces.
- Funding
- German Research Foundation (DFG)
- Partners
- Universität Passau (Tobias Harks)
Applications
Energy Systems
Optimization models for the design and operation of energy systems, including coupled transport and supply networks.
Energy Markets
Equilibrium and bilevel models for market design, pricing, and strategic decisions in electricity and gas markets.
Machine Learning & Data-Driven Optimization
Mixed-integer, bilevel, and robust optimization methods for learning, classification, clustering, and data-informed decisions.
Infrastructure & Networks
Network optimization for planning and operating infrastructure, with a focus on energy transport networks.