Team > AD Dr. Robert Baier

Faculty of Mathematics, Physics and Computer Sciences
Department of Mathematics

AD Dr. Robert Baier
Academic Director, Senior Lecturer
webmaster of the Chair (and of the Mathematical Institute until 27 April 2022)
in the local organisation committee of the MTNS 2022

contact data

research priorities

projects

profiles

Faculty of Mathematics, Physics and Computer Sciences
Department of Mathematics

• Set-valued numerics (esp. interpolation, integration, approximation, selections and fixed points of set-valued maps)
  
• Differential inclusions (esp. reachable sets at a given time, approximation of trajectories, discontinuous differential equations, impulsive systems)
  
• Optimal control problems and control theory (esp. direct discretization methods, convergence of discretization methods, numerical computation of Lyapunov functions and invariant sets)
  
• Convex analysis (esp. representation of sets, arithmetic set operations, difference of convex sets and functins (DC), embeddings of convex compacts into a Banach space)
  
• Nonsmooth optimization (esp. nonconvex subdifferentials, DC and quasidifferentiable functions, optimality conditions)
  
• see also the web page with the visualization
  

my running projects

• Nonconvex subdifferentials in nonsmooth optimization
• Set-valued numerical analysis

my finished projects

• edition of the series “Bayreuther Mathematischen Schriften (BMS)”
• ITN SADCO "Optimal control approaches to reachability analysis: safety & avoidance" (Task 2.5)

Faculty of Mathematics, Physics and Computer Sciences
Department of Mathematics

Publications sorted by years (Publications sorted by types)

2023

Articles in a journal    ↑ top

Robert Baier and Elza Farkhi: A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. In: Computational Optimization and Applications, 86 (2023). - S. 885-923.
doi:10.1007/s10589-023-00517-9

2022

Articles in a journal    ↑ top

Robert Baier, Gabriele Eichfelder and Tobias Gerlach: Optimality conditions for set optimization using a directional derivative based on generalized Steiner sets. In: Optimization, 71 (2022). - S. 2273-2314.
doi:10.1080/02331934.2020.1812605

2021

Articles in a journal    ↑ top

Wolfgang Riedl, Robert Baier and Matthias Gerdts: Optimization-based subdivision algorithm for reachable sets. In: Journal of Computational Dynamics, 8 (2021). - S. 99-130.
doi:10.3934/jcd.2021005

2020

Articles in a journal    ↑ top

Ilaria Xausa, Robert Baier, Olivier Bokanowski and Matthias Gerdts: Computation of avoidance regions for driver assistance systems by using a Hamilton-Jacobi approach. In: Optimal Control Applications and Methods, 41 (2020). - S. 668-689.
doi:10.1002/oca.2565

2019

Articles in a journal    ↑ top

Robert Baier and Thuy Thi Thien Le: Construction of the Minimum Time Function for Linear Systems Via Higher-Order Set-Valued Methods. In: Mathematical Control and Related Fields, 9 (2019). - S. 223-255.
doi:10.3934/mcrf.2019012

Robert Baier, Philipp Braun, Lars Grüne and Christopher M. Kellett: Numerical Calculation of Nonsmooth Control Lyapunov Functions via Piecewise Affine Approximation. In: IFAC-PapersOnLine, 52 (2019). - S. 370-375.
doi:10.1016/j.ifacol.2019.11.808

2018

Book chapters & Conference proceedings    ↑ top

Robert Baier and Elza Farkhi: Discrete Filippov-type stability for one-sided Lipschitzian difference inclusions. In: Gustav Feichtinger, Raimund M. Kovacevic, Gernot Tragler (Hrsg.): Control Systems and Mathematical Methods in Economics : Essays in Honor of Vladimir M. Veliov. - Cham : Springer, 2018. - S. 27-55.
doi:10.1007/978-3-319-75169-6_3

Robert Baier, Philipp Braun, Lars Grüne and Christopher M. Kellett: Numerical construction of nonsmooth control Lyapunov functions. In: Pontus Giselsson, Anders Rantzer (Hrsg.): Large-Scale and Distributed Optimization. - Cham : Springer, 2018. - S. 343-373.
doi:10.1007/978-3-319-97478-1_12

2017

Articles in a journal    ↑ top

Wolfgang Achtziger, Robert Baier, Elza Farkhi and Vera Roshchina: Exact Penalty and Lagrange Duality via the Directed Subdifferential. In: Pure and Applied Functional Analysis, 2 (2017). - S. 183-220.

Preprints & Working papers    ↑ top

Wolfgang Riedl, Robert Baier and Matthias Gerdts: Analytical and numerical estimates of reachable sets in a subdivision scheme.. - Bayreuth ; Neubiberg/München, 2017-05-03. - 15 S.
doi:10.15495/EPub_UBT_00005055

2016

Articles in a journal    ↑ top

Robert Baier, Elza Farkhi and Vera Roshchina: From Quasidifferentiable to Directed Subdifferentiable Functions : Exact Calculus Rules. In: Journal of Optimization Theory and Applications, 171 (2016). - S. 384-401.
doi:10.1007/s10957-016-0926-x

2015

Articles in a journal    ↑ top

Huijuan Li, Robert Baier, Lars Grüne, Sigurdur Freyr Hafstein and Fabian Wirth: Computation of local ISS Lyapunov functions with low gains via linear programming. In: Discrete and Continuous Dynamical Systems. Series B, 20 (2015). - S. 2477-2495.
doi:10.3934/dcdsb.2015.20.2477

Preprints & Working papers    ↑ top

Robert Baier and Thuy Thi Thien Le: Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 1: Error Estimates.. - Bayreuth ; Padova, 2015-12. - 30 S.

Robert Baier and Thuy Thi Thien Le: Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 2: Numerical Computations.. - Bayreuth ; Padova, 2015-12. - 16 S.

2014

Articles in a journal    ↑ top

Robert Baier, Michael Dellnitz, Mirko Hessel-von Molo, Yannis G. Kevrekidis and Stefan Sertl: The computation of convex invariant sets via Newton's method. In: Journal of Computational Dynamics, 1 (2014). - S. 39-69.
doi:10.3934/jcd.2014.1.39

Robert Baier, Elza Farkhi and Vera Roshchina: Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure. In: Journal of Optimization Theory and Applications, 160 (2014). - S. 391-414.
doi:10.1007/s10957-013-0401-x

Elza Farkhi, Tzanko D. Donchev and Robert Baier: Existence of Solutions for Nonconvex Differential Inclusions of Monotone Type. In: Comptes Rendus de l'Académie Bulgare des Sciences, 67 (2014). - S. 323-330.

Book chapters & Conference proceedings    ↑ top

Huijuan Li, Robert Baier, Lars Grüne, Sigurdur Freyr Hafstein and Fabian Wirth: Computation of local ISS Lyapunov functions via linear programming. In: MTNS 2014 : MTNS 2014 : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. - Groningen : University of Groningen Press, 2014. - S. 1189-1195.

Robert Baier and Sigurdur Freyr Hafstein: Numerical computation of control Lyapunov functions in the sense of generalized gradients. In: MTNS 2014 : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. - Groningen : University of Groningen Press, 2014. - S. 1173-1180.

Further publications    ↑ top

Ilaria Xausa, Robert Baier, Olivier Bokanowski, Matthias Gerdts and Daniel Töpfer: Software for verification of collision avoidance algorithms via optimal control techniques. - (Vortrag), Veranstaltung: Conference on New Trends in Optimal Control (NetCO 2014), 23.-27. Juni 2014, Tours, Frankreich.

2013

Articles in a journal    ↑ top

Robert Baier, Matthias Gerdts and Ilaria Xausa: Approximation of reachable sets using optimal control algorithms. In: Numerical Algebra, Control and Optimization, 3 (2013). - S. 519-548.
doi:10.3934/naco.2013.3.519

Walter Alt, Robert Baier, Frank Lempio and Matthias Gerdts: Approximations of linear control problems with bang-bang solutions. In: Optimization, 62 (2013). - S. 9-32.
doi:10.1080/02331934.2011.568619

Robert Baier and Elza Farkhi: Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity. In: Serdica Mathematical Journal, 39 (2013). - S. 365-390.

Robert Baier and Elza Farkhi: Regularity of set-valued maps and their selections through set differences. Part 2: One-sided Lipschitz properties. In: Serdica Mathematical Journal, 39 (2013). - S. 391-422.

2012

Articles in a journal    ↑ top

Robert Baier, Elza Farkhi and Vera Roshchina: The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I : Definition and examples. In: Nonlinear Analysis : Theory, Methods & Applications, 75 (2012). - S. 1074-1088.
doi:10.1016/j.na.2011.04.074

Robert Baier, Elza Farkhi and Vera Roshchina: The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II : Calculus. In: Nonlinear Analysis : Theory, Methods & Applications, 75 (2012). - S. 1058-1073.
doi:10.1016/j.na.2011.04.073

Walter Alt, Robert Baier, Matthias Gerdts and Frank Lempio: Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions. In: Numerical Algebra, Control and Optimization, 2 (2012). - S. 547-570.
doi:10.3934/naco.2012.2.547

Robert Baier, Q. Din and T. D. Donchev: Higher order Runge–Kutta methods for impulsive differential systems. In: Applied Mathematics and Computation, 218 (2012). - S. 11790-11798.
doi:10.1016/j.amc.2012.05.037

Robert Baier, Lars Grüne and Sigurđur Freyr Hafstein: Linear programming based Lyapunov function computation for differential inclusions. In: Discrete and Continuous Dynamical Systems. Series B, 17 (2012). - S. 33-56.
doi:10.3934/dcdsb.2012.17.33

Book chapters & Conference proceedings    ↑ top

Ilaria Xausa, Robert Baier, Matthias Gerdts, Mark Gonter and Christian Wegwerth: Avoidance trajectories for driver assistance systems via solvers for optimal control problems. In: Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), July 9-13, 2012, Melbourne, Australia. - Melbourne, Australia : Think Business Events, 2012. - S. 8.

Robert Baier and Mirko Hessel-von Molo: Newton’s method and secant method for set-valued mappings. In: Ivan Lirkov, Svetozar D. Margenov, Jerzy Waśniewski (Hrsg.): Large-scale scientific computing : 8th international conference, LSSC 2011, Sozopol, Bulgaria, June 6 - 10, 2011 ; revised selected papers. - Berlin : 2012. - S. 91-98.
doi:10.1007/978-3-642-29843-1_9

Robert Baier: Set-valued Euler's method with interpolated distance functions and optimal control solvers. In: Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012). - Melbourne, Australia : Think Business Events, 2012.

2011

Articles in a journal    ↑ top

Robert Baier and Gilbert Perria: Set-valued Hermite interpolation. In: Journal of Approximation Theory, 163 (2011). - S. 1349-1372.
doi:10.1016/j.jat.2010.11.004

2010

Articles in a journal    ↑ top

Robert Baier, Lars Grüne and Sigurdur Freyr Hafstein: Computing Lyapunov functions for strongly asymptotically stable differential inclusions. In: IFAC Proceedings Volumes, 43 (2010). - S. 1098-1103.
doi:10.3182/20100901-3-IT-2016.00132

Robert Baier and Tzanko Donchev: Discrete Approximation of Impulsive Differential Inclusions. In: Numerical Functional Analysis and Optimization, 31 (2010). - S. 653-678.
doi:10.1080/01630563.2010.483878

Book chapters & Conference proceedings    ↑ top

Robert Baier and Elza Farkhi: The Directed Subdifferential of DC functions. In: A. Leizaarowitz, B. S. Mordukhovich, I. Shafrir, A. J. Zaslavski (Hrsg.): Nonlinear analysis and optimization II. Optimization : a conference in celebration of Alex Ioffe's 70th and Simeon Reich's 60th birthdays, June 18-24, 2008, Haifa, Israel. - Providence, R.I. : American Mathematical Society, 2010. - S. 27-43.
doi:10.1090/conm/514

Robert Baier, Elza Farkhi and Vera Roshchina: On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions. In: Regina S. Burachik, Jen-Chih Yao (Hrsg.): Variational Analysis and Generalized Differentiation in Optimization and Control : In Honor of Boris S. Mordukhovich. - New York : Springer, 2010. - S. 59-93.
doi:10.1007/978-1-4419-0437-9_3

2009

Book chapters & Conference proceedings    ↑ top

Robert Baier and Matthias Gerdts: A computational method for non-convex reachable sets using optimal control. In: Proceedings of the European Control Conference (ECC). - Piscataway, New Jersey : IEEE, 2009. - S. 97-102.
doi:10.23919/ECC.2009.7074386

Preprints & Working papers    ↑ top

Robert Baier and Tzanko Donchev: Discrete Approximation of Impulsive Differential Inclusions.. - Bonn, 2009. - 22 S.

2008

Articles in a journal    ↑ top

Robert Baier and Frank Lempio: Von Eudoxos bis zur Klimafolgenforschung : Exhaustion, Finite Elemente und mengenwertige Numerik. In: Spektrum, (2008). - S. 6-12.

Preprints & Working papers    ↑ top

Robert Baier and Gilbert Perria: Hermite Interpolation with Directed Sets.. - Bonn, 2008-12. -

Robert Baier and Elza Farkhi: The Directed Subdifferential of DC functions.. - Bonn, 2008-03. - 19 S.

2007

Articles in a journal    ↑ top

Robert Baier, Christof Büskens, Ilyes Aïssa Chahma and Matthias Gerdts: Approximation of reachable sets by direct solution methods for optimal control problems. In: Optimization Methods and Software, 22 (2007). - S. 433-452.
doi:10.1080/10556780600604999

Robert Baier and Elza Farkhi: Regularity and Integration of Set-Valued Maps Represented by Generalized Steiner Points. In: Set-Valued Analysis, 15 (2007). - S. 185-207.
doi:10.1007/s11228-006-0038-0

Robert Baier, Ilyes Aïssa Chahma and Frank Lempio: Stability and Convergence of Euler's Method for State-Constrained Differential Inclusions. In: SIAM Journal on Optimization, 18 (2007). - S. 1004-1026.
doi:10.1137/060661867

Book chapters & Conference proceedings    ↑ top

Robert Baier: Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis. In: Vasile Staicu (Hrsg.): Differential Equations, Chaos and Variational Problems. - Basel : Birkhäuser, 2007. - S. 49-60.
doi:10.1007/978-3-7643-8482-1_4

2005

Books/Monographs    ↑ top

Robert Baier and Matthias Gerdts: Set-Valued Numerical Analysis and Optimal Control : Lecture Notes for the DAAD Intensive Course "Optimization - Theory and Applications" (July 05 -17, 2005). - Borovets, Bulgaria : 2005. - 264 S.

Book chapters & Conference proceedings    ↑ top

Robert Baier: Selection Strategies for Set-Valued Runge-Kutta Methods. In: Zhilin Li, Lubin Vulkov, Jerzy Waśniewski (Hrsg.): Numerical Analysis and Its Applications : Third International Conference, NAA 2004, Rousse, Bulgaria, June 29-July 3, 2004 ; Revised Selected Papers. - Berlin ; Heidelberg : Springer, 2005. - S. 149-157.
doi:10.1007/978-3-540-31852-1_16

2004

Preprints & Working papers    ↑ top

Robert Baier and N. Dyn: Rotational Metric Average in |R^n. - Bayreuth, 2004. -

Robert Baier: Selection Strategies of Set-Valued Runge-Kutta Methods. - Bayreuth, 2004. -

2002

Book chapters & Conference proceedings    ↑ top

Robert Baier, N. Dyn and E. Farkhi: The Metric Average of 1D Compact Sets. In: Charles K. Chui, Larry L. Schumaker, Joachim Stöckler (Hrsg.): Approximation Theory X : selections of papers that were presented at the Tenth International Conference on Approximation Theory, held in St. Louis, Missouri, in March 2001. Volume 1. Abstract and classical analysis. - Nashville : Vanderbilt Univ. Press, 2002. - S. 9-22.

Preprints & Working papers    ↑ top

Robert Baier, Frank Lempio and Evgenii S. Polovinkin: Set-Valued Integration with Negative Weights. - Bayreuth, 2002.

2001

Articles in a journal    ↑ top

Robert Baier and Elza M. Farkhi: Differences of Convex Compact Sets in the Space of Directed Sets. Part I: The Space of Directed Sets. In: Set-Valued Analysis, 9 (2001). - S. 217-245.
doi:10.1023/A:1012046027626

Robert Baier and Elza M. Farkhi: Differences of Convex Compact Sets in the Space of Directed Sets. Part II: Visualization of Directed Sets. In: Set-Valued Analysis, 9 (2001). - S. 247-272.
doi:10.1023/A:1012009529492

Book chapters & Conference proceedings    ↑ top

Robert Baier and Elza M. Farkhi: Directed Derivatives of Convex Compact-Valued Mappings. In: Nicolas Hadjisavvas, Panos M. Pardalos (Hrsg.): Advances in Convex Analysis and Global Optimization : honoring the memory of C. Caratheodory (1873 - 1950). - Dordrecht : Kluwer Academic Publishers, 2001. - S. 501-514.
doi:10.1007/978-1-4613-0279-7_32

1999

Book chapters & Conference proceedings    ↑ top

Robert Baier and E. Farkhi: Directed Sets and Differences of Convex Compact Sets. In: Michael P. Polis, Asen L. Dontchev, Peter Kall, Irena Lasiecka, Andrzej W. Olbrot (Hrsg.): Systems modelling and optimization : Proceedings of the 18th IFIP TC7 Conference held in Detroit, Michigan, July 22-25, 1997. - Boca Raton : Chapman & Hall, 1999. - S. 135-143.

1995

Books/Monographs    ↑ top

Robert Baier: Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen. - Bayreuth : Universität, 1995.

1994

Articles in a journal    ↑ top

Robert Baier: Extrapolation Methods for the Computation of Set-Valued Integrals and Reachable Sets of Linear Differential Inclusions. In: ZAMM : Journal of Applied Mathematics and Mechanics = Zeitschrift für angewandte Mathematik und Mechanik, 74 (1994). - .
doi:10.1002/zamm.19940740604

Book chapters & Conference proceedings    ↑ top

Robert Baier and Frank Lempio: Approximating Reachable Sets by Extrapolation Methods. In: Pierre-Jean Laurent, Alain Le Méhauteé, Larry L. Schumaker (Hrsg.): Curves and Surfaces in Geometric Design : Papers from the Second International Conference on Curves and Surfaces, held in Chamonix-Mont-Blanc, France, July 10-16, 1993. - Wellesley, Mass. : Peters, 1994. - S. 9-18.

Robert Baier and Frank Lempio: Computing Aumann's Integral. In: Aleksandr B. Kuržanskij, Vladimir M. Veliov (Hrsg.): Modeling Techniques for Uncertain Systems : Proceedings of a Conference held in Sopron, Hungary, July 6-10, 1992. - Basel : Birkhäuser, 1994. - S. 71-92.

Thesis    ↑ top

Robert Baier:Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen. - Bayreuth: Department of Mathematics, 1994. - XIX, 202 S. S.
(Dissertation, 1994, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

1990

Thesis    ↑ top

Robert Baier: Konvergenz und numerische Realisierung von Mehrgitterverfahren und Diskretisierungsmethoden für Randwertaufgaben zweiter Ordnung. - Bayreuth, 1990. XIX, 202 S.
(Diplomarbeit, 1990, Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Faculty of Mathematics, Physics and Computer Sciences
Department of Mathematics

AD Dr. Robert Baier
Academic Director, Senior Lecturer

University of Bayreuth
Chair of Applied Mathematics
Universitätsstraße 30
95440 Bayreuth, Germany