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Funding: German Science Foundation (DFG) as part of the project “SFB Transregio 154”
Abstract: The goal of this subproject is to develop mathematical methods to solve mixed-integer and nonlinear multilevel optimization problems for gas markets coupled with markets of other energy sectors such as electricity. Motivated by the two cases of cooperating or non-cooperating network operators of the different sectors, we investigate on the one hand bilevel problems with potentially multiple solutions on the lower level, for which we establish methods to assess pessimistic solutions. On the other hand, we study multi-leader-follower games and develop problem-tailored solution approaches. Finally, based on our mathematical and algorithmic developments, we characterize equilibria in coupled energy systems for different combinations of market designs in the considered sectors.
Project manager: Veronika Grimm, Julia Grübel and Alexander Martin
Staff: Martin Loy
Project term: 01.07.2022 – 30.06.2026 (Phase 3), 01.10.2016 – 30.06.2022 (Phase 1 and 2)
Publications:
- Grimm, V., Grübel, J., Schewe, L., Schmidt, M., & Zöttl, G. (2019). Nonconvex Equilibrium Models for Gas Market Analysis: Failure of Standard Techniques and Alternative Modeling Approaches. European Journal of Operational Research, 273(3), 1097-1108. https://doi.org/10.1016/j.ejor.2018.09.016
- Grimm, V., Schewe, L., Schmidt, M., & Zöttl, G. (2017). Uniqueness of market equilibrium on a network: A peak-load pricing approach. European Journal of Operational Research, 261(3), 971 - 983. https://doi.org/10.1016/j.ejor.2017.03.036
- Grimm, V., Schewe, L., Schmidt, M., & Zöttl, G. (2019). A multilevel model of the European entry-exit gas market. Mathematical Methods of Operations Research, 89(2), 223–255. https://doi.org/10.1007/s00186-018-0647-z
- Kleinert, T., & Schmidt, M. (2020). Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method. Informs Journal on Computing. https://doi.org/10.1287/ijoc.2019.0945
- Kleinert, T., Schmidt, M., Plein, F., & Labbé, M. (2020). There's No Free Lunch: On the Hardness of Choosing a Correct Big-M in Bilevel Optimization. Operations Research, 68(6), 1625-1931. https://doi.org/10.1287/opre.2019.1944
- Kleinert, T., Grimm, V., & Schmidt, M. (2021). Outer Approximation for Global Optimization of Mixed-Integer Quadratic Bilevel Problems. Mathematical Programming. https://doi.org/10.1007/s10107-020-01601-2
- Kleinert, T., Schmidt, M., Labbé, M., & Plein, F. (2020). Closing the Gap in Linear Bilevel Optimization: A New Valid Primal-Dual Inequality. Optimization Letters. https://doi.org/10.1007/s11590-020-01660-6
- Kleinert, T., Manns, J., Schmidt, M., & Weninger, D. (2021). Presolving Linear Bilevel Optimization Problems. EURO Journal on Computational Optimization. https://doi.org/10.1016/j.ejco.2021.100020
- Kleinert, T. (2021). Algorithms for Mixed-Integer Bilevel Problems with Convex Followers (Dissertation).
- Boettger, T., Grimm, V., Kleinert, T., & Schmidt, M. (2022). The cost of decoupling trade and transport in the European entry-exit gas market with linear physics modeling. European Journal of Operational Research, 297(3), 1095-1111. https://doi.org/10.1016/j.ejor.2021.06.034
- Grimm, V., Nowak, D., Schewe, L., Schmidt, M., Schwartz, A., & Zöttl, G. (2021). A tractable multi-leader multi-follower peak-load-pricing model with strategic interaction. Mathematical Programming. https://doi.org/10.1007/s10107-021-01708-0
- Grimm, V., Hintermüller, M., Huber, O., Schewe, L., Schmidt, M., & Zöttl, G. (2021). A PDE-Constrained Generalized Nash Equilibrium Approach for Modeling Gas Markets with Transport.
- Egerer, J., Grimm, V., Grübel, J., & Zöttl, G. (2022). Long-run market equilibria in coupled energy sectors: A study of uniqueness. European Journal of Operational Research, 303(3), 1335-1354. https://doi.org/10.1016/j.ejor.2022.03.028
- Heitsch, H., Henrion, R., Kleinert, T., & Schmidt, M. (2022). On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints. Journal of Global Optimization. https://doi.org/10.1007/s10898-022-01161-z
- Grübel, J., Huber, O., Hümbs, L., Klimm, M., Schmidt, M., & Schwartz, A. (2023). Nonconvex equilibrium models for energy markets: exploiting price information to determine the existence of an equilibrium. Optimization Methods & Software, 38(1), 153-183. https://doi.org/10.1080/10556788.2022.2117358
- Kleinert, T., & Schmidt, M. (2023). Why there is no need to use a big-M in linear bilevel optimization: a computational study of two ready-to-use approaches. Computational Management Science, 20(1). https://doi.org/10.1007/s10287-023-00435-5
- Grübel, J. (2022). Existence, Uniqueness, and Algorithms for Equilibria in Competitive Energy Markets (Dissertation).
- Grübel, J., Krug, R., Schmidt, M., & Wollner, W. (2023). A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities. Journal of Optimization Theory and Applications, 198, 1077-1117. https://doi.org/10.1007/s10957-023-02254-9
- Grimm, V., Grübel, J., Schmidt, M., Schwartz, A., Zöttl, G., & Wiertz, A.-K. (2023). On a Tractable Single-Level Reformulation of a Multilevel Model of the European Entry-Exit Gas Market with Market Power.
Thürauf, J., Grübel, J., & Schmidt, M. (2024). Adjustable Robust Nonlinear Network Design under Demand Uncertainties.
Further publications of the subproject can be found at https://opus4.kobv.de/opus4-trr154/home