Kleinert, Thomas; Schmidt, Martin Why there is no need to use a big-\(M\) in linear bilevel optimization: a computational study of two ready-to-use approaches. (English) Zbl 07778007 Comput. Manag. Sci. 20, Paper No. 3, 12 p. (2023). MSC: 90Bxx 90Cxx 90-08 90C11 90C46 PDFBibTeX XMLCite \textit{T. Kleinert} and \textit{M. Schmidt}, Comput. Manag. Sci. 20, Paper No. 3, 12 p. (2023; Zbl 07778007) Full Text: DOI
Grübel, Julia; Krug, Richard; Schmidt, Martin; Wollner, Winnifried A successive linear relaxation method for MINLPs with multivariate Lipschitz continuous nonlinearities. (English) Zbl 07739329 J. Optim. Theory Appl. 198, No. 3, 1077-1117 (2023). MSC: 90C11 90C26 90C30 90C90 PDFBibTeX XMLCite \textit{J. Grübel} et al., J. Optim. Theory Appl. 198, No. 3, 1077--1117 (2023; Zbl 07739329) Full Text: DOI arXiv
Beck, Yasmine; Ljubić, Ivana; Schmidt, Martin A survey on bilevel optimization under uncertainty. (English) Zbl 07737877 Eur. J. Oper. Res. 311, No. 2, 401-426 (2023). MSC: 90Bxx PDFBibTeX XMLCite \textit{Y. Beck} et al., Eur. J. Oper. Res. 311, No. 2, 401--426 (2023; Zbl 07737877) Full Text: DOI
De Santis, Marianna; de Vries, Sven; Schmidt, Martin; Winkel, Lukas A penalty branch-and-bound method for mixed binary linear complementarity problems. (English) Zbl 07640784 INFORMS J. Comput. 34, No. 6, 3117-3133 (2022). MSC: 90Cxx PDFBibTeX XMLCite \textit{M. De Santis} et al., INFORMS J. Comput. 34, No. 6, 3117--3133 (2022; Zbl 07640784) Full Text: DOI
Heitsch, Holger; Henrion, René; Kleinert, Thomas; Schmidt, Martin On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints. (English) Zbl 1505.90140 J. Glob. Optim. 84, No. 3, 651-685 (2022). MSC: 90C46 90C90 90B15 PDFBibTeX XMLCite \textit{H. Heitsch} et al., J. Glob. Optim. 84, No. 3, 651--685 (2022; Zbl 1505.90140) Full Text: DOI
Krebs, Vanessa; Schmidt, Martin \(\Gamma\)-robust linear complementarity problems. (English) Zbl 1501.90100 Optim. Methods Softw. 37, No. 2, 658-691 (2022). MSC: 90C33 90C17 91B50 91A10 90C34 PDFBibTeX XMLCite \textit{V. Krebs} and \textit{M. Schmidt}, Optim. Methods Softw. 37, No. 2, 658--691 (2022; Zbl 1501.90100) Full Text: DOI
Plein, Fränk; Thürauf, Johannes; Labbé, Martine; Schmidt, Martin A bilevel optimization approach to decide the feasibility of bookings in the European gas market. (English) Zbl 1493.90039 Math. Methods Oper. Res. 95, No. 3, 409-449 (2022). MSC: 90B10 90C11 90C35 90B06 90C05 65K05 90C10 90C26 PDFBibTeX XMLCite \textit{F. Plein} et al., Math. Methods Oper. Res. 95, No. 3, 409--449 (2022; Zbl 1493.90039) Full Text: DOI
Schmidt, Martin; Sirvent, Mathias; Wollner, Winnifried The cost of not knowing enough: mixed-integer optimization with implicit Lipschitz nonlinearities. (English) Zbl 1492.90095 Optim. Lett. 16, No. 5, 1355-1372 (2022). MSC: 90C11 90C30 PDFBibTeX XMLCite \textit{M. Schmidt} et al., Optim. Lett. 16, No. 5, 1355--1372 (2022; Zbl 1492.90095) Full Text: DOI
Schewe, Lars; Schmidt, Martin; Thürauf, Johannes Global optimization for the multilevel European gas market system with nonlinear flow models on trees. (English) Zbl 1486.90060 J. Glob. Optim. 82, No. 3, 627-653 (2022). MSC: 90B10 90B06 90C26 90C35 90C11 90C30 PDFBibTeX XMLCite \textit{L. Schewe} et al., J. Glob. Optim. 82, No. 3, 627--653 (2022; Zbl 1486.90060) Full Text: DOI
Böttger, T.; Grimm, V.; Kleinert, T.; Schmidt, M. The cost of decoupling trade and transport in the European entry-exit gas market with linear physics modeling. (English) Zbl 1490.91147 Eur. J. Oper. Res. 297, No. 3, 1095-1111 (2022). MSC: 91B74 90B10 90C11 90C17 PDFBibTeX XMLCite \textit{T. Böttger} et al., Eur. J. Oper. Res. 297, No. 3, 1095--1111 (2022; Zbl 1490.91147) Full Text: DOI
Labbé, Martine; Plein, Fränk; Schmidt, Martin; Thürauf, Johannes Deciding feasibility of a booking in the European gas market on a cycle is in P for the case of passive networks. (English) Zbl 07775323 Networks 78, No. 2, 128-152 (2021). MSC: 91B74 PDFBibTeX XMLCite \textit{M. Labbé} et al., Networks 78, No. 2, 128--152 (2021; Zbl 07775323) Full Text: DOI OA License
Kleinert, Thomas; Labbé, Martine; Ljubić, Ivana; Schmidt, Martin A survey on mixed-integer programming techniques in bilevel optimization. (English) Zbl 07711228 EURO J. Comput. Optim. 9, Article ID 100007, 21 p. (2021). Reviewer: Ritu Arora (Delhi) MSC: 90-02 90-08 90Bxx 91A65 90C11 90C26 90C46 90C33 90C90 PDFBibTeX XMLCite \textit{T. Kleinert} et al., EURO J. Comput. Optim. 9, Article ID 100007, 21 p. (2021; Zbl 07711228) Full Text: DOI
Krug, Richard; Mehrmann, Volker; Schmidt, Martin Nonlinear optimization of district heating networks. (English) Zbl 1492.90174 Optim. Eng. 22, No. 2, 783-819 (2021). MSC: 90C30 90C35 90C90 90B10 PDFBibTeX XMLCite \textit{R. Krug} et al., Optim. Eng. 22, No. 2, 783--819 (2021; Zbl 1492.90174) Full Text: DOI arXiv
Gabriel, Steven A.; Leal, Marina; Schmidt, Martin Solving binary-constrained mixed complementarity problems using continuous reformulations. (English) Zbl 1510.90270 Comput. Oper. Res. 131, Article ID 105208, 12 p. (2021). MSC: 90C33 90C11 PDFBibTeX XMLCite \textit{S. A. Gabriel} et al., Comput. Oper. Res. 131, Article ID 105208, 12 p. (2021; Zbl 1510.90270) Full Text: DOI
Kleinert, Thomas; Schmidt, Martin Computing feasible points of bilevel problems with a penalty alternating direction method. (English) Zbl 07362311 INFORMS J. Comput. 33, No. 1, 198-215 (2021). MSC: 90Cxx PDFBibTeX XMLCite \textit{T. Kleinert} and \textit{M. Schmidt}, INFORMS J. Comput. 33, No. 1, 198--215 (2021; Zbl 07362311) Full Text: DOI
Schewe, Lars; Schmidt, Martin; Thürauf, Johannes Computing technical capacities in the European entry-exit gas market is NP-hard. (English) Zbl 1451.90032 Ann. Oper. Res. 295, No. 1, 337-362 (2020). MSC: 90B10 90C35 90C60 90C90 PDFBibTeX XMLCite \textit{L. Schewe} et al., Ann. Oper. Res. 295, No. 1, 337--362 (2020; Zbl 1451.90032) Full Text: DOI
Schewe, Lars; Schmidt, Martin The impact of potential-based physics models on pricing in energy networks. (English) Zbl 07252396 CEJOR, Cent. Eur. J. Oper. Res. 28, No. 3, 1003-1029 (2020). MSC: 90Bxx PDFBibTeX XMLCite \textit{L. Schewe} and \textit{M. Schmidt}, CEJOR, Cent. Eur. J. Oper. Res. 28, No. 3, 1003--1029 (2020; Zbl 07252396) Full Text: DOI
Schewe, Lars; Schmidt, Martin; Thürauf, Johannes Structural properties of feasible bookings in the European entry-exit gas market system. (English) Zbl 1442.90019 4OR 18, No. 2, 197-218 (2020). MSC: 90B06 90B10 90C11 90C05 90C30 PDFBibTeX XMLCite \textit{L. Schewe} et al., 4OR 18, No. 2, 197--218 (2020; Zbl 1442.90019) Full Text: DOI
Labbé, Martine; Plein, Fränk; Schmidt, Martin Bookings in the European gas market: characterisation of feasibility and computational complexity results. (English) Zbl 1433.90030 Optim. Eng. 21, No. 1, 305-334 (2020). MSC: 90B06 90B10 90C30 90C35 90C39 90C90 PDFBibTeX XMLCite \textit{M. Labbé} et al., Optim. Eng. 21, No. 1, 305--334 (2020; Zbl 1433.90030) Full Text: DOI Link
Hante, Falk M.; Schmidt, Martin Complementarity-based nonlinear programming techniques for optimal mixing in gas networks. (English) Zbl 1431.90017 EURO J. Comput. Optim. 7, No. 3, 299-323 (2019). MSC: 90B06 90C20 90C11 90C30 PDFBibTeX XMLCite \textit{F. M. Hante} and \textit{M. Schmidt}, EURO J. Comput. Optim. 7, No. 3, 299--323 (2019; Zbl 1431.90017) Full Text: DOI
Schmidt, Martin; Sirvent, Mathias; Wollner, Winnifried A decomposition method for MINLPs with Lipschitz continuous nonlinearities. (English) Zbl 1426.90053 Math. Program. 178, No. 1-2 (A), 449-483 (2019). MSC: 90B06 90B10 90C11 90C30 90C90 PDFBibTeX XMLCite \textit{M. Schmidt} et al., Math. Program. 178, No. 1--2 (A), 449--483 (2019; Zbl 1426.90053) Full Text: DOI
Robinius, Martin; Schewe, Lars; Schmidt, Martin; Stolten, Detlef; Thürauf, Johannes; Welder, Lara Robust optimal discrete arc sizing for tree-shaped potential networks. (English) Zbl 1414.90240 Comput. Optim. Appl. 73, No. 3, 791-819 (2019). MSC: 90C11 90B10 90C35 90C90 90C60 PDFBibTeX XMLCite \textit{M. Robinius} et al., Comput. Optim. Appl. 73, No. 3, 791--819 (2019; Zbl 1414.90240) Full Text: DOI
Grimm, Veronika; Schewe, Lars; Schmidt, Martin; Zöttl, Gregor A multilevel model of the European entry-exit gas market. (English) Zbl 1415.90012 Math. Methods Oper. Res. 89, No. 2, 223-255 (2019). MSC: 90B10 90C11 91B55 90C30 PDFBibTeX XMLCite \textit{V. Grimm} et al., Math. Methods Oper. Res. 89, No. 2, 223--255 (2019; Zbl 1415.90012) Full Text: DOI
Geißler, Björn; Morsi, Antonio; Schewe, Lars; Schmidt, Martin Solving highly detailed gas transport MINLPs: block separability and penalty alternating direction methods. (English) Zbl 1446.90053 INFORMS J. Comput. 30, No. 2, 309-323 (2018). MSC: 90B06 90C30 90C26 90C11 PDFBibTeX XMLCite \textit{B. Geißler} et al., INFORMS J. Comput. 30, No. 2, 309--323 (2018; Zbl 1446.90053) Full Text: DOI Link
Mehrmann, Volker; Schmidt, Martin; Stolwijk, Jeroen J. Model and discretization error adaptivity within stationary gas transport optimization. (English) Zbl 1406.35254 Vietnam J. Math. 46, No. 4, 779-801 (2018). MSC: 35Q31 65G99 65L70 90C30 93C40 76N15 PDFBibTeX XMLCite \textit{V. Mehrmann} et al., Vietnam J. Math. 46, No. 4, 779--801 (2018; Zbl 1406.35254) Full Text: DOI arXiv
Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. (English) Zbl 1391.49040 Comput. Optim. Appl. 70, No. 1, 267-294 (2018). MSC: 49K20 49J15 49J20 76B75 90C11 90C35 PDFBibTeX XMLCite \textit{M. Gugat} et al., Comput. Optim. Appl. 70, No. 1, 267--294 (2018; Zbl 1391.49040) Full Text: DOI
Schmidt, Martin; Steinbach, Marc C.; Willert, Bernhard M. High detail stationary optimization models for gas networks: validation and results. (English) Zbl 1364.90067 Optim. Eng. 17, No. 2, 437-472 (2016). MSC: 90B10 90C30 90C06 90C90 PDFBibTeX XMLCite \textit{M. Schmidt} et al., Optim. Eng. 17, No. 2, 437--472 (2016; Zbl 1364.90067) Full Text: DOI
Rose, Daniel; Schmidt, Martin; Steinbach, Marc C.; Willert, Bernhard M. Computational optimization of gas compressor stations: MINLP models versus continuous reformulations. (English) Zbl 1354.90008 Math. Methods Oper. Res. 83, No. 3, 409-444 (2016). MSC: 90-08 90C11 90C30 90C33 90C90 PDFBibTeX XMLCite \textit{D. Rose} et al., Math. Methods Oper. Res. 83, No. 3, 409--444 (2016; Zbl 1354.90008) Full Text: DOI Link
Schmidt, Martin; Steinbach, Marc C.; Willert, Bernhard M. High detail stationary optimization models for gas networks. (English) Zbl 1364.90066 Optim. Eng. 16, No. 1, 131-164 (2015). MSC: 90B10 90C06 90C30 90C90 90C35 PDFBibTeX XMLCite \textit{M. Schmidt} et al., Optim. Eng. 16, No. 1, 131--164 (2015; Zbl 1364.90066) Full Text: DOI
Schmidt, Martin An interior-point method for nonlinear optimization problems with locatable and separable nonsmoothness. (English) Zbl 1329.90144 EURO J. Comput. Optim. 3, No. 4, 309-348 (2015). MSC: 90C30 90C51 90C90 90C35 90C56 90B10 PDFBibTeX XMLCite \textit{M. Schmidt}, EURO J. Comput. Optim. 3, No. 4, 309--348 (2015; Zbl 1329.90144) Full Text: DOI
Pfetsch, Marc E.; Fügenschuh, Armin; Geißler, Björn; Geißler, Nina; Gollmer, Ralf; Hiller, Benjamin; Humpola, Jesco; Koch, Thorsten; Lehmann, Thomas; Martin, Alexander; Morsi, Antonio; Rövekamp, Jessica; Schewe, Lars; Schmidt, Martin; Schultz, Rüdiger; Schwarz, Robert; Schweiger, Jonas; Stangl, Claudia; Steinbach, Marc C.; Vigerske, Stefan; Willert, Bernhard M. Validation of nominations in gas network optimization: models, methods, and solutions. (English) Zbl 1325.90019 Optim. Methods Softw. 30, No. 1, 15-53 (2015). MSC: 90B15 90B10 90C90 90C11 90B90 PDFBibTeX XMLCite \textit{M. E. Pfetsch} et al., Optim. Methods Softw. 30, No. 1, 15--53 (2015; Zbl 1325.90019) Full Text: DOI