Publications "Baier, Robert"

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Number of items: 62.

Book / Monograph

Baier, Robert ; Gerdts, Matthias:
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 p.

Baier, Robert:
Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen.
Bayreuth : Universität , 1995 . - XXII, 248 S. - (Bayreuther Mathematische Schriften ; 50 )

Review:

Article in a journal

Baier, Robert ; Farkhi, Elza:
A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions.
In: Computational Optimization and Applications. (11 September 2023) . - pp. 1-39.
ISSN 0926-6003
DOI: https://doi.org/10.1007/s10589-023-00517-9

Riedl, Wolfgang ; Baier, Robert ; Gerdts, Matthias:
Optimization-based subdivision algorithm for reachable sets.
In: Journal of Computational Dynamics. Vol. 8 (2021) Issue 1 . - pp. 99-130.
ISSN 2158-2491
DOI: https://doi.org/10.3934/jcd.2021005

Baier, Robert ; Eichfelder, Gabriele ; Gerlach, Tobias:
Optimality conditions for set optimization using a directional derivative based on generalized Steiner sets.
In: Optimization. (14 September 2020) . - pp. 1-42.
ISSN 0323-3898
DOI: https://doi.org/10.1080/02331934.2020.1812605

Xausa, Ilaria ; Baier, Robert ; Bokanowski, Olivier ; Gerdts, Matthias:
Computation of avoidance regions for driver assistance systems by using a Hamilton-Jacobi approach.
In: Optimal Control Applications and Methods. Vol. 41 (2020) Issue 2 . - pp. 668-689.
ISSN 1099-1514
DOI: https://doi.org/10.1002/oca.2565

Review:

Baier, Robert ; Le, Thuy Thi Thien:
Construction of the Minimum Time Function for Linear Systems Via Higher-Order Set-Valued Methods.
In: Mathematical Control and Related Fields. Vol. 9 (2019) Issue 2 . - pp. 223-255.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2019012

Review:

Baier, Robert ; Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Numerical Calculation of Nonsmooth Control Lyapunov Functions via Piecewise Affine Approximation.
In: IFAC-PapersOnLine. Vol. 52 (2019) Issue 16 . - pp. 370-375.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2019.11.808

Achtziger, Wolfgang ; Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
Exact Penalty and Lagrange Duality via the Directed Subdifferential.
In: Pure and Applied Functional Analysis. Vol. 2 (2017) Issue 2 . - pp. 183-220.
ISSN 2189-3756

Review:

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
From Quasidifferentiable to Directed Subdifferentiable Functions : Exact Calculus Rules.
In: Journal of Optimization Theory and Applications. Vol. 171 (2016) Issue 2 . - pp. 384-401.
ISSN 0022-3239
DOI: https://doi.org/10.1007/s10957-016-0926-x

Review:

Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions with low gains via linear programming.
In: Discrete and Continuous Dynamical Systems. Series B. Vol. 20 (2015) Issue 8 . - pp. 2477-2495.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2015.20.2477

Review:

Baier, Robert ; Dellnitz, Michael ; Hessel-von Molo, Mirko ; Kevrekidis, Yannis G. ; Sertl, Stefan:
The computation of convex invariant sets via Newton's method.
In: Journal of Computational Dynamics. Vol. 1 (2014) Issue 1 . - pp. 39-69.
ISSN 2158-2491
DOI: https://doi.org/10.3934/jcd.2014.1.39

Review:

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure.
In: Journal of Optimization Theory and Applications. Vol. 160 (2014) Issue 2 . - pp. 391-414.
ISSN 0022-3239
DOI: https://doi.org/10.1007/s10957-013-0401-x

Review:

Farkhi, Elza ; Donchev, Tzanko D. ; Baier, Robert:
Existence of Solutions for Nonconvex Differential Inclusions of Monotone Type.
In: Comptes Rendus de l'Académie Bulgare des Sciences. Vol. 67 (2014) Issue 3 . - pp. 323-330.
ISSN 1310-1331

Review:

Baier, Robert ; Gerdts, Matthias ; Xausa, Ilaria:
Approximation of reachable sets using optimal control algorithms.
In: Numerical Algebra, Control and Optimization. Vol. 3 (September 2013) Issue 3 . - pp. 519-548.
ISSN 2155-3297
DOI: https://doi.org/10.3934/naco.2013.3.519

Review:

Alt, Walter ; Baier, Robert ; Lempio, Frank ; Gerdts, Matthias:
Approximations of linear control problems with bang-bang solutions.
In: Optimization. Vol. 62 (2013) Issue 1 . - pp. 9-32.
ISSN 0233-1934
DOI: https://doi.org/10.1080/02331934.2011.568619

Review:

Baier, Robert ; Farkhi, Elza:
Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity.
In: Serdica Mathematical Journal. Vol. 39 (2013) Issue 3-4 . - pp. 365-390.
ISSN 1310-6600

Review:

Baier, Robert ; Farkhi, Elza:
Regularity of set-valued maps and their selections through set differences. Part 2: One-sided Lipschitz properties.
In: Serdica Mathematical Journal. Vol. 39 (2013) Issue 3-4 . - pp. 391-422.
ISSN 1310-6600

Review:

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I : Definition and examples.
In: Nonlinear Analysis : Theory, Methods & Applications. Vol. 75 (2012) Issue 3 . - pp. 1074-1088.
ISSN 0362-546X
DOI: https://doi.org/10.1016/j.na.2011.04.074

Review:

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II : Calculus.
In: Nonlinear Analysis : Theory, Methods & Applications. Vol. 75 (2012) Issue 3 . - pp. 1058-1073.
ISSN 0362-546X
DOI: https://doi.org/10.1016/j.na.2011.04.073

Review:

Alt, Walter ; Baier, Robert ; Gerdts, Matthias ; Lempio, Frank:
Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions.
In: Numerical Algebra, Control and Optimization. Vol. 2 (2012) Issue 3 . - pp. 547-570.
ISSN 2155-3297
DOI: https://doi.org/10.3934/naco.2012.2.547

Review:

Baier, Robert ; Din, Q. ; Donchev, T. D.:
Higher order Runge–Kutta methods for impulsive differential systems.
In: Applied Mathematics and Computation. Vol. 218 (2012) Issue 24 . - pp. 11790-11798.
ISSN 0096-3003
DOI: https://doi.org/10.1016/j.amc.2012.05.037

Review:

Baier, Robert ; Grüne, Lars ; Freyr Hafstein, Sigurđur:
Linear programming based Lyapunov function computation for differential inclusions.
In: Discrete and Continuous Dynamical Systems. Series B. Vol. 17 (2012) Issue 1 . - pp. 33-56.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2012.17.33

Review:

Baier, Robert ; Perria, Gilbert:
Set-valued Hermite interpolation.
In: Journal of Approximation Theory. Vol. 163 (2011) Issue 10 . - pp. 1349-1372.
ISSN 1096-0430
DOI: https://doi.org/10.1016/j.jat.2010.11.004

Review:

Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr:
Computing Lyapunov functions for strongly asymptotically stable differential inclusions.
In: IFAC Proceedings Volumes. Vol. 43 (2010) Issue 14 . - pp. 1098-1103.
ISSN 1474-6670
DOI: https://doi.org/10.3182/20100901-3-IT-2016.00132

Baier, Robert ; Donchev, Tzanko:
Discrete Approximation of Impulsive Differential Inclusions.
In: Numerical Functional Analysis and Optimization. Vol. 31 (2010) Issue 6 . - pp. 653-678.
ISSN 1532-2467
DOI: https://doi.org/10.1080/01630563.2010.483878

Review:

Baier, Robert ; Lempio, Frank:
Von Eudoxos bis zur Klimafolgenforschung : Exhaustion, Finite Elemente und mengenwertige Numerik.
In: Spektrum. (2008) Issue 1 . - pp. 6-12.

Baier, Robert ; Farkhi, Elza:
Regularity and Integration of Set-Valued Maps Represented by Generalized Steiner Points.
In: Set-Valued Analysis. Vol. 15 (March 2007) Issue 2 . - pp. 185-207.
ISSN 0927-6947
DOI: https://doi.org/10.1007/s11228-006-0038-0

Review:

Baier, Robert ; Büskens, Christof ; Chahma, Ilyes Aïssa ; Gerdts, Matthias:
Approximation of reachable sets by direct solution methods for optimal control problems.
In: Optimization Methods and Software. Vol. 22 (2007) Issue 3 . - pp. 433-452.
ISSN 1029-4937
DOI: https://doi.org/10.1080/10556780600604999

Review:

Baier, Robert ; Chahma, Ilyes Aïssa ; Lempio, Frank:
Stability and Convergence of Euler's Method for State-Constrained Differential Inclusions.
In: SIAM Journal on Optimization. Vol. 18 (2007) Issue 3 . - pp. 1004-1026.
ISSN 1095-7189
DOI: https://doi.org/10.1137/060661867

Review:

Baier, Robert ; Farkhi, Elza M.:
Differences of Convex Compact Sets in the Space of Directed Sets. Part I: The Space of Directed Sets.
In: Set-Valued Analysis. Vol. 9 (September 2001) Issue 3 . - pp. 217-245.
ISSN 0927-6947
DOI: https://doi.org/10.1023/A:1012046027626

Review:

Baier, Robert ; Farkhi, Elza M.:
Differences of Convex Compact Sets in the Space of Directed Sets. Part II: Visualization of Directed Sets.
In: Set-Valued Analysis. Vol. 9 (September 2001) Issue 3 . - pp. 247-272.
ISSN 0927-6947
DOI: https://doi.org/10.1023/A:1012009529492

Review:

Baier, Robert:
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. Vol. 74 (1994) Issue 6 . - S. T55-T557.
ISSN 1521-4001
DOI: https://doi.org/10.1002/zamm.19940740604

Review:

Article in a book

Baier, Robert ; Farkhi, Elza:
Discrete Filippov-type stability for one-sided Lipschitzian difference inclusions.
In: Feichtinger, Gustav ; Kovacevic, Raimund M. ; Tragler, Gernot (ed.): Control Systems and Mathematical Methods in Economics : Essays in Honor of Vladimir M. Veliov. - Cham : Springer , 2018 . - pp. 27-55 . - (Lecture Notes in Economics and Mathematical Systems ; 687 )
ISBN 978-3-319-75168-9
DOI: https://doi.org/10.1007/978-3-319-75169-6_3

Review:

Baier, Robert ; Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Numerical construction of nonsmooth control Lyapunov functions.
In: Giselsson, Pontus ; Rantzer, Anders (ed.): Large-Scale and Distributed Optimization. - Cham : Springer , 2018 . - pp. 343-373 . - (Lecture Notes in Mathematics ; 2227 )
ISBN 978-3-319-97477-4
DOI: https://doi.org/10.1007/978-3-319-97478-1_12

Review:

Li, Huijuan ; Baier, Robert ; Grüne, Lars ; Hafstein, Sigurdur Freyr ; Wirth, Fabian:
Computation of local ISS Lyapunov functions via linear programming.
In: MTNS 2014 : Proceedings on the 21st International Symposium on Mathematical Theory of Networks and Systems, July 7--11, 2014, University of Groningen. - Groningen , 2014 . - pp. 1189-1195
ISBN 978-90-367-6321-9

Baier, Robert ; Hafstein, Sigurdur Freyr:
Numerical computation of control Lyapunov functions in the sense of generalized gradients.
In: MTNS 2014 : 21st International Symposium on Mathematical Theory of Networks and Systems, July 7-11, 2014, Groningen, The Netherlands ; Proceedings. - Groningen : University of Groningen , 2014 . - pp. 1173-1180
ISBN 978-90-367-6321-9

Xausa, Ilaria ; Baier, Robert ; Gerdts, Matthias ; Gonter, Mark ; Wegwerth, Christian:
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 . - p. 8
ISBN 978-0-646-58062-3

Baier, Robert ; Hessel-von Molo, Mirko:
Newton’s method and secant method for set-valued mappings.
In: Lirkov, Ivan ; Margenov, Svetozar D. ; Waśniewski, Jerzy (ed.): Large-scale scientific computing : 8th international conference, LSSC 2011, Sozopol, Bulgaria, June 6 - 10, 2011 ; revised selected papers. - Berlin , 2012 . - pp. 91-98 . - (Lecture Notes in Computer Science ; 7116 )
ISBN 978-3-642-29842-4
DOI: https://doi.org/10.1007/978-3-642-29843-1_9

Review:

Baier, Robert:
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
ISBN 978-0-646-58062-3

Baier, Robert ; Farkhi, Elza:
The Directed Subdifferential of DC functions.
In: Leizaarowitz, A. ; Mordukhovich, B. S. ; Shafrir, I. ; Zaslavski, A. J. (ed.): 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 . - pp. 27-43 . - (Contemporary Mathematics ; 514 )
ISBN 9780821881934
DOI: https://doi.org/10.1090/conm/514

Review:

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions.
In: Burachik, Regina S. ; Yao, Jen-Chih (ed.): Variational Analysis and Generalized Differentiation in Optimization and Control : In Honor of Boris S. Mordukhovich. - New York : Springer , 2010 . - pp. 59-93 . - (Springer Optimization and its Applications ; 47 )
ISBN 978-1-4419-0436-2
DOI: https://doi.org/10.1007/978-1-4419-0437-9_3

Review:

Baier, Robert ; Gerdts, Matthias:
A computational method for non-convex reachable sets using optimal control.
In: Proceedings of the European Control Conference (ECC). - Piscataway, New Jersey : IEEE , 2009 . - pp. 97-102
ISBN 978-3-9524173-9-3
DOI: https://doi.org/10.23919/ECC.2009.7074386

Baier, Robert:
Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis.
In: Staicu, Vasile (ed.): Differential Equations, Chaos and Variational Problems. - Basel : Birkhäuser , 2007 . - pp. 49-60 . - (Progress in Nonlinear Differential Equations and Their Applications ; 75 )
ISBN 978-3-7643-8481-4
DOI: https://doi.org/10.1007/978-3-7643-8482-1_4

Review:

Baier, Robert:
Selection Strategies for Set-Valued Runge-Kutta Methods.
In: Li, Zhilin ; Vulkov, Lubin ; Waśniewski, Jerzy (ed.): Numerical Analysis and Its Applications : Third International Conference, NAA 2004, Rousse, Bulgaria, June 29-July 3, 2004 ; Revised Selected Papers. - Berlin ; Heidelberg : Springer , 2005 . - pp. 149-157 . - (Lecture Notes in Computer Science ; 3401 )
ISBN 978-3-540-24937-5
DOI: https://doi.org/10.1007/978-3-540-31852-1_16

Review:

Baier, Robert ; Dyn, N. ; Farkhi, E.:
The Metric Average of 1D Compact Sets.
In: Chui, Charles K. ; Schumaker, Larry L. ; Stöckler, Joachim (ed.): 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 . - pp. 9-22 . - (Innovations in Applied Mathematics )
ISBN 0-8265-1415-4

Review:

Baier, Robert ; Farkhi, Elza M.:
Directed Derivatives of Convex Compact-Valued Mappings.
In: Hadjisavvas, Nicolas ; Pardalos, Panos M. (ed.): Advances in Convex Analysis and Global Optimization : honoring the memory of C. Caratheodory (1873 - 1950). - Dordrecht : Kluwer Academic Publishers , 2001 . - pp. 501-514 . - (Nonconvex Optimization and its Applications ; 54 )
ISBN 978-0-7923-6942-4
DOI: https://doi.org/10.1007/978-1-4613-0279-7_32

Review:

Baier, Robert ; Farkhi, E.:
Directed Sets and Differences of Convex Compact Sets.
In: Polis, Michael P. ; Dontchev, Asen L. ; Kall, Peter ; Lasiecka, Irena ; Olbrot, Andrzej W. (ed.): Systems modelling and optimization : Proceedings of the 18th IFIP TC7 Conference held in Detroit, Michigan, July 22-25, 1997. - Boca Raton : Chapman & Hall , 1999 . - pp. 135-143 . - (Chapman & Hall/CRC Research Notes in Mathematics Series ; 396 )
ISBN 0-8493-0607-8

Review:

Baier, Robert ; Lempio, Frank:
Approximating Reachable Sets by Extrapolation Methods.
In: Laurent, Pierre-Jean ; Le Méhauteé, Alain ; Schumaker, Larry L. (ed.): 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 . - pp. 9-18
ISBN 1-56881-039-3

Review:

Baier, Robert ; Lempio, Frank:
Computing Aumann's Integral.
In: Kuržanskij, Aleksandr B. ; Veliov, Vladimir M. (ed.): Modeling Techniques for Uncertain Systems : Proceedings of a Conference held in Sopron, Hungary, July 6-10, 1992. - Basel : Birkhäuser , 1994 . - pp. 71-92 . - (Progress in Systems and Control Theory ; 18 )
ISBN 3-7643-3746-X

Review:

Conference item

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

Preprint, postprint

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

Baier, Robert ; Le, Thuy Thi Thien:
Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 1: Error Estimates.
University of Bayreuth, Germany; Università di Padova, Italy
Bayreuth ; Padova , 2015 . - 30 p.

Baier, Robert ; Le, Thuy Thi Thien:
Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 2: Numerical Computations.
University of Bayreuth, Germany; Università di Padova, Italy
Bayreuth ; Padova , 2015 . - 16 p.

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

Baier, Robert ; Perria, Gilbert:
Hermite Interpolation with Directed Sets.
Hausdorff-Research-Institute
Bonn , 2008 . - 35 S.

Baier, Robert ; Farkhi, Elza:
The Directed Subdifferential of DC functions.
Hausdorff-Research-Institute
Bonn , 2008 . - 19 p.

Working paper, discussion paper

Baier, Robert ; Dyn, N.:
Rotational Metric Average in |R^n.
Bayreuth : Mathematisches Institut , 2004 . - 11 S. - (Technical Report )

Baier, Robert:
Selection Strategies of Set-Valued Runge-Kutta Methods.
Bayreuth : Mathematisches Institut , 2004 . - 40 S. - (Technical Report )

Project report, research report, expert assessments

Baier, Robert ; Lempio, Frank ; Polovinkin, Evgenii S.:
Set-Valued Integration with Negative Weights.
Bayreuth : Mathematisches Institut, 2002 . - 35 S.

Doctoral thesis

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

Master's, Magister, Diploma, or Admission thesis

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

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