Pablos, Blanca; Gerdts, Matthias Substructure exploitation of a nonsmooth Newton method for large-scale optimal control problems with full discretization. (English) Zbl 07431535 Math. Comput. Simul. 190, 641-658 (2021). MSC: 65-XX 90-XX PDFBibTeX XMLCite \textit{B. Pablos} and \textit{M. Gerdts}, Math. Comput. Simul. 190, 641--658 (2021; Zbl 07431535) Full Text: DOI
Martens, Björn; Gerdts, Matthias Convergence analysis for approximations of optimal control problems subject to higher index differential-algebraic equations and pure state constraints. (English) Zbl 1466.49028 SIAM J. Control Optim. 59, No. 3, 1903-1926 (2021). MSC: 49M25 34A09 47H14 49J15 49J30 49K15 PDFBibTeX XMLCite \textit{B. Martens} and \textit{M. Gerdts}, SIAM J. Control Optim. 59, No. 3, 1903--1926 (2021; Zbl 1466.49028) Full Text: DOI
Gottschalk, Simon; Burger, Michael; Gerdts, Matthias A projected primal-dual gradient optimal control method for deep reinforcement learning. (English) Zbl 1472.49042 J. Math. Ind. 10, Paper No. 9, 22 p. (2020). MSC: 49K15 90C40 93E35 60J20 68Q06 PDFBibTeX XMLCite \textit{S. Gottschalk} et al., J. Math. Ind. 10, Paper No. 9, 22 p. (2020; Zbl 1472.49042) Full Text: DOI
Martens, Björn; Gerdts, Matthias Error analysis for the implicit Euler discretization of linear-quadratic control problems with higher index DAEs and bang-bang solutions. (English) Zbl 1451.49021 Reis, Timo (ed.) et al., Progress in differential-algebraic equations II. Proceedings of the 9th workshop on descriptor systems, Paderborn, Germany, March 17–20, 2019. Cham: Springer. Differ.-Algebr. Equ. Forum, 291-330 (2020). MSC: 49K15 49J15 49N10 34A09 49M25 49J30 PDFBibTeX XMLCite \textit{B. Martens} and \textit{M. Gerdts}, in: Progress in differential-algebraic equations II. Proceedings of the 9th workshop on descriptor systems, Paderborn, Germany, March 17--20, 2019. Cham: Springer. 291--330 (2020; Zbl 1451.49021) Full Text: DOI
Martens, Björn; Gerdts, Matthias Convergence analysis for approximations of optimal control problems subject to higher index differential-algebraic equations and mixed control-state constraints. (English) Zbl 1431.49025 SIAM J. Control Optim. 58, No. 1, 1-33 (2020). MSC: 49K15 49M25 34A09 65L80 PDFBibTeX XMLCite \textit{B. Martens} and \textit{M. Gerdts}, SIAM J. Control Optim. 58, No. 1, 1--33 (2020; Zbl 1431.49025) Full Text: DOI
Burger, Michael; Gerdts, Matthias DAE aspects in vehicle dynamics and mobile robotics. (English) Zbl 1447.93227 Campbell, Stephen (ed.) et al., Applications of differential-algebraic equations: examples and benchmarks. Cham: Springer. Differ.-Algebr. Equ. Forum, 37-80 (2019). MSC: 93C85 93C15 34A09 PDFBibTeX XMLCite \textit{M. Burger} and \textit{M. Gerdts}, in: Applications of differential-algebraic equations: examples and benchmarks. Cham: Springer. 37--80 (2019; Zbl 1447.93227) Full Text: DOI
Samà, Marcella; D’Ariano, Andrea; Palagachev, Konstantin; Gerdts, Matthias Integration methods for aircraft scheduling and trajectory optimization at a busy terminal manoeuvring area. (English) Zbl 1527.90107 OR Spectrum 41, No. 3, 641-681 (2019). MSC: 90B35 90C11 90C29 49K15 49N90 PDFBibTeX XMLCite \textit{M. Samà} et al., OR Spectrum 41, No. 3, 641--681 (2019; Zbl 1527.90107) Full Text: DOI
Martens, Björn; Gerdts, Matthias Convergence analysis of the implicit Euler-discretization and sufficient conditions for optimal control problems subject to index-one differential-algebraic equations. (English) Zbl 1419.49007 Set-Valued Var. Anal. 27, No. 2, 405-431 (2019). MSC: 49J15 49K15 65L20 65L80 PDFBibTeX XMLCite \textit{B. Martens} and \textit{M. Gerdts}, Set-Valued Var. Anal. 27, No. 2, 405--431 (2019; Zbl 1419.49007) Full Text: DOI
Kimmerle, S.-J.; Gerdts, M.; Herzog, R. Optimal control of an elastic crane-trolley-load system – a case study for optimal control of coupled ODE-PDE systems. (English) Zbl 1486.49002 Math. Comput. Model. Dyn. Syst. 24, No. 2, 182-206 (2018). MSC: 49J15 49J20 74B05 PDFBibTeX XMLCite \textit{S. J. Kimmerle} et al., Math. Comput. Model. Dyn. Syst. 24, No. 2, 182--206 (2018; Zbl 1486.49002) Full Text: DOI
Huber, Andreas; Gerdts, Matthias; Bertolazzi, Enrico Structure exploitation in an interior-point method for fully discretized, state constrained optimal control problems. (English) Zbl 1405.49020 Vietnam J. Math. 46, No. 4, 1089-1113 (2018). MSC: 49M25 49J15 90C51 90C06 PDFBibTeX XMLCite \textit{A. Huber} et al., Vietnam J. Math. 46, No. 4, 1089--1113 (2018; Zbl 1405.49020) Full Text: DOI
Dreves, Axel; Gerdts, Matthias A generalized Nash equilibrium approach for optimal control problems of autonomous cars. (English) Zbl 1390.49046 Optim. Control Appl. Methods 39, No. 1, 326-342 (2018). MSC: 49N70 91A10 34H05 PDFBibTeX XMLCite \textit{A. Dreves} and \textit{M. Gerdts}, Optim. Control Appl. Methods 39, No. 1, 326--342 (2018; Zbl 1390.49046) Full Text: DOI
Burger, Michael; Gerdts, Matthias A survey on numerical methods for the simulation of initial value problems with sDAEs. (English) Zbl 1402.65085 Ilchmann, Achim (ed.) et al., Surveys in differential-algebraic equations IV. Cham: Springer (ISBN 978-3-319-46617-0/pbk; 978-3-319-46618-7/ebook). Differential-Algebraic Equations Forum, 221-300 (2017). MSC: 65L80 65L06 65-02 PDFBibTeX XMLCite \textit{M. Burger} and \textit{M. Gerdts}, in: Surveys in differential-algebraic equations IV. Cham: Springer. 221--300 (2017; Zbl 1402.65085) Full Text: DOI
Gaitsgory, Vladimir; Gerdts, Matthias On numerical solution of singularly perturbed optimal control problems. (English) Zbl 1391.49004 J. Optim. Theory Appl. 174, No. 3, 762-784 (2017). Reviewer: Aygul Manapova (Ufa) MSC: 49J15 65L11 49M25 PDFBibTeX XMLCite \textit{V. Gaitsgory} and \textit{M. Gerdts}, J. Optim. Theory Appl. 174, No. 3, 762--784 (2017; Zbl 1391.49004) Full Text: DOI
Landry, Chantal; Welz, Wolfgang; Gerdts, Matthias Combining discrete and continuous optimization to solve kinodynamic motion planning problems. (English) Zbl 1364.49053 Optim. Eng. 17, No. 3, 533-556 (2016). MSC: 49N90 49M25 49J15 70E60 90C30 90C35 93C85 PDFBibTeX XMLCite \textit{C. Landry} et al., Optim. Eng. 17, No. 3, 533--556 (2016; Zbl 1364.49053) Full Text: DOI
Kimmerle, Sven-Joachim; Gerdts, Matthias Numerical optimal control of a coupled ODE-PDE model of a truck with a fluid basin. (English) Zbl 1336.35295 Discrete Contin. Dyn. Syst. 2015, Suppl., 515-524 (2015). MSC: 35Q35 49J15 49J20 35L04 49N90 76B15 35L65 90C20 PDFBibTeX XMLCite \textit{S.-J. Kimmerle} and \textit{M. Gerdts}, Discrete Contin. Dyn. Syst. 2015, 515--524 (2015; Zbl 1336.35295) Full Text: DOI
Gerdts, Matthias A survey on optimal control problems with differential-algebraic equations. (English) Zbl 1331.49001 Ilchmann, Achim (ed.) et al., Surveys in differential-algebraic equations II. Cham: Springer (ISBN 978-3-319-11049-3/pbk; 978-3-319-11050-9/ebook). Differential-Algebraic Equations Forum, 103-161 (2015). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 49-02 49K15 49K21 49M25 49M05 49M15 49N10 34A09 65L80 PDFBibTeX XMLCite \textit{M. Gerdts}, in: Surveys in differential-algebraic equations II. Cham: Springer. 103--161 (2015; Zbl 1331.49001) Full Text: DOI
Palagachev, Konstantin; Gerdts, Matthias Mathematical programs with blocks of vanishing constraints arising in discretized mixed-integer optimal control problems. (English) Zbl 1312.49036 Set-Valued Var. Anal. 23, No. 1, 149-167 (2015). MSC: 49M25 49M20 90C11 49J15 49N90 65K05 90C30 PDFBibTeX XMLCite \textit{K. Palagachev} and \textit{M. Gerdts}, Set-Valued Var. Anal. 23, No. 1, 149--167 (2015; Zbl 1312.49036) Full Text: DOI