Overview on Recent Papers

Baier, Robert:

Mengenwertige Integration und die diskrete Approximation erreichbarer Mengen,
Bayreuther Mathematische Schriften 50 (1995).

Baier, Robert:

Extrapolation Methods for the Computation of Set-Valued Integrals and Reachable Sets of Linear Differential Inclusions,
ZAMM 74 (1994), No. 6, T555-557.

Baier, Robert:

Generalized Steiner Selections Applied to Standard Problems of Set-Valued Numerical Analysis
in: V. Staicu (ed.): Differential Equations, Chaos and Variational Problems, Progress in Nonlinear Differential Equations and Their Applications 75. Birkhäuser, Basel, 2007, pp. 49-60.

Baier, Robert:

Selection Strategies for Set-Valued Runge-Kutta Methods
in: Zhilin Li, Lubin G. Vulkov, Jerzy Wasniewski (eds.): Numerical Analysis and Its Applications, Third International Conference, NAA 2004, Rousse, Bulgaria, June 29 - July 3, 2004, Revised Selected Papers. Lecture Notes in Computer Science 3401. Springer-Verlag, Berlin-Heidelberg, 2005, pp. 149-157.

Baier, Robert; Büskens, Christof; Chahma, Ilyes Aïssa and Gerdts, Matthias:

Approximation of Reachable Sets by Direct Solution Methods of Optimal Control Problems,
Optimization Methods and Software 22 (3), 2007, pp. 433-452.

Baier, Robert; Chahma, Ilyes Aïssa and Lempio, Frank:

Stability and Convergence of Euler's Method to State-Constrained Differential Inclusions,
SIAM Journal on Optimization 18 (3), 2007, pp. 1004-1026. Special issue on "Variational Analysis and Optimization".

Baier, Robert, Dyn, Nira, and Farkhi, Elza:

The metric average of 1D Compact Sets
in: Charles K. Chui, Larry L. Schumaker, and Joachim Stoeckler (eds.): Approximation Theory X, St. Louis, Missouri, March 26-29, 2001, Vanderbilt University Press, Nashville, TN, 2001, 15 pages.

Baier, Robert and Farkhi, Elza:

Directed Sets and Differences of Convex Compact Sets,
in: Michael P. Polis, Asen L. Dontchev, Peter Kall, Irena Lasiecka, Andrzej W. Olbrot (eds.): Systems Modelling and Optimization, Proceedings of the 18^th IFIP TC7 Conference 1997, Pitman Research Notes in Mathematics Series, 396. Chapman and Hall/CRC, 1999, pp. 135-143.

Baier, Robert and Farkhi, Elza:

Differences of Convex Compact Sets in the Space of Directed Sets - Part I: The Space of Directed Sets,
Set-Valued Analysis 9 (3), 2001, pp. 217-245.

Baier, Robert and Farkhi, Elza:

Differences of Convex Compact Sets in the Space of Directed Sets - Part II: Visualization of Directed Sets,
Set-Valued Analysis 9 (3), 2001, pp. 247-272.

Baier, Robert and Farkhi, Elza:

Directed Derivatives of Convex Compact-Valued Mappings,
in: Nicolas Hajisavvas, Panos M. Pardalos (eds), Advances in Convex Analysis and Global Optimization: honoring the memory of C. Caratheodory (1873-1950), Nonconvex Optimization and Its Applications Vol. 54, Kluwer Academic Publishers, Dordrecht-Boston-London, 2001, pp. 501-514.

Baier, Robert and Farkhi, Elza:

Regularity and Integration of Set-Valued Maps Represented by Generalized Steiner Points,
Set-Valued Analysis 15 (2), 2007, pp. 185-206.

Baier, Robert and Farkhi, Elza:

The Directed Subdifferential of DC Functions,
to appear in: Proceedings on the Conference on Nonlinear Analysis and Optimization in celebration of Alex Ioffe's 70th and Simeon Reich's 60th birthdays, June 18-24, Technion, Haifa, Israel, 2008, 20 pages.

Baier, Robert and Gerdts, Matthias:

Set-Valued Numerical Analysis and Optimal Control,
Lecture Notes for the DAAD Intensive Course "Optimization – Theory and Applications" in Borovets/Sofia, Bulgaria, July 05-17, Bayreuth-Hamburg, 2005, 264 p.

Baier, Robert and Lempio, Frank:

Approximating Reachable Sets by Extrapolation Methods,
in: P.J. Laurent, A. Le Mehaute and L.L. Schumaker (eds.): Curves and Surfaces in Geometric Design, Wellesley: A K Peters, 1994, pp. 9-18.

Baier, Robert and Lempio, Frank:

Computing Aumann's Integral,
in: Kurzhanski, A. B. and Veliov, V. (eds.): Modeling Techniques for Uncertain Systems, Proceedings of a Conferences held in Sopron (Hungary), July 6-10, 1992, Progress in Systems and Control Theory 18, Basel: Birkhäuser, 1994, pp. 71-92.

Büskens, Christof and Gerdts, Matthias:

Numerical Solution of Optimal Control Problems with DAE Systems of Higher Index,
Proceedings of the Workshop "Optimalsteuerungsprobleme in der Luft- und Raumfahrt" in Greifswald, Sonderforschungsbereich 255: Transatmosphärische Flugsysteme, Technische Universität München, 2000.

Büskens, Christof and Gerdts, Matthias:

Real-time Optimization of DAE Systems,
in: M. Grötschel, S. O. Krumke and J. Rambau (eds.), 'Online Optimization of Large Scale Systems', pp. 117-128, Springer, 2001.

Büskens, Christof and Gerdts, Matthias:

Emergency Landing of a Hypersonic Flight System: A Corrector Iteration Method for admissible Real-Time Optimal Control Approximations,
Proceedings of the workshop 'Optimal Control' at Greifswald, SFB 255: Transatmosphärische Flugsysteme, Hieronymus, München, pp. 51-60, 2003.

Chahma, Ilyes Aïssa:

Set-Valued Discrete Approximation of State-Constrained Differential Inclusions,
Bayreuther Mathematische Schriften 67 (2003), p. 3-162.

Chudej, Kurt; Büskens, Christof and Graf, Tobias:

Solution of a Hard Flight Path Optimization Problem by Different Optimization Codes High-Performance Scientific and Computing Engineering,
Lecture Notes in Computational Science and Engineering, Vol. 21, Springer, New York, pp.289-296, 2002.

Dontchev, Asen and Lempio, Frank:

Difference Methods for Differential Inclusions: A Survey,
SIAM Review, Vol. 34, No. 2, 1992, pp. 263-294.

Gerdts, Matthias:

Numerische Methoden optimaler Steuerprozesse mit differential-algebraischen Gleichungssystemen höheren Indexes und ihre Anwendungen in der Kraftfahrzeugsimulation und Mechanik,
Bayreuther Mathematische Schriften, Band 61, Bayreuth, 2001.

Gerdts, Matthias:

Numerical Treatment of Optimal Control Problems with Differential-Algebraic Equations and Applications to Virtual Test-drives,
in: M. Anile, V. Capasso, A. Greco (Eds.), 'Progress in Industrial Mathematics at ECMI 2000', Vol. 1 of 'Mathematics in Industry', pp. 549-553, Springer, 2002.

Gerdts, Matthias:

Direct Shooting Method for the Numerical Solution of Higher Index DAE Optimal Control Problems,
Journal of Optimization Theory and Applications 117 (2), pp. 267-294, 2003.

Gerdts, Matthias:

A Moving Horizon Technique in Vehicle Simulation,
ZAMM 83 (3), pp. 147-162, 2003.

Gerdts, Matthias:

Optimal Control and Real-Time Optimization of Mechanical Multi-Body Systems,
ZAMM 83 (10), pp. 705-719, 2003.

Gerdts, Matthias:

Parameter Optimization in Mechanical Multibody Systems and Linearized Runge-Kutta Methods,
in: A. Buikis; R. Ciegis, A.D. Flitt (Eds.), 'Progress in Industrial Mathematics at ECMI 2002', Vol. 5 of 'Mathematics in Industry', pp. 121-126, Springer, 2004.

Gerdts, Matthias and Büskens, Christof:

Computation of Consistent Initial Values for Optimal Control Problems with DAE Systems of Higher Index,
ZAMM, 81 S2, pp. 249-250, 2001.

Gerdts, Matthias and Büskens, Christof:

Consistent Initialization of Sensitivity Matrices for a Class of Parametric DAE Systems,
BIT 42:4, pp. 796-813.

Graf, Tobias:

Flugbahnoptimierung eines Niedrig-Schub-Raumfahrzeugs,
Diplomarbeit, Universität Bayreuth, Mai 2001, 75 S.

Hörnlein, Herbert und Schittkowski, Klaus (eds.):

Software Systems for Structural Optimization,
International Series of Numerical Mathematics, Vol. 110, Birkhäuser, 1992.

Kastner-Maresch, Alois and Krivan, Vlastimil:

Modelling Food Preferences and Viability Constraints,
Journal of Biological Systems 3 (1995), pp. 313-322.

Kastner-Maresch, Alois and Lempio, Frank:

Difference Methods with Selection Strategies for Differential Inclusions,
Numer. Funct. Anal. and Optimiz. Vol. 14, No. 5 & 6, 1993, pp. 555-572.

Kastner-Maresch, Alois and Mooney, Harold A.:

Simulating Optimal Plant Biomass Partitioning
Ecological Modelling 75/76 (1994), pp. 309-320.

Kastner-Maresch, Alois:

Implicit Runge-Kutta methods for differential inclusions,
Numer. Funct. Anal. and Optimiz. 11, 1991, 937-958.

Kastner-Maresch, Alois:

The Implicit Midpoint Rule Applied to Discontinuous Differential Equations,
Computing 49, 1992, pp. 45-62.

Lempio, Frank and Osmolovskii, Nikolai:

Jacobi conditions and Riccati equation for broken extremal
(in Russian),
Modern Mathematics and its Applications, volume 60, 1998, 187-215. English translation is available.

Lempio, Frank and Osmolovskii, Nikolai:

Jacobi-type Conditions and Riccati Equation for Broken Extremal,
(English translation from the Russian), Journal of Mathematical Sciences, Vol. 100, No. 5, 2000, pp. 2572-2592.

Lempio, Frank and Silin, Dimitry B.:

Generalized differential equations with strongly one-sided Lipschitzian right-hand side.
(English. Russian original) Differential Equations 32, No.11, 1996, pp. 1485-1491; translation from Differ. Uravn. 32, No. 11, 1996, pp. 1488-1494.

Lempio, Frank and Veliov, Vladimir:

Discrete Approximations of Differential Inclusions.
GAMM-Mitteilungen 21, Heft 2, 1998, pp. 103-135.

Lempio, Frank:

Über zwei Jahrtausende Finite Elemente - von Eudoxos bis zur Hyperthermietherapie,
27. Kolloquium Mathematik-Didaktik an der Universität Bayreuth, 18. Febr. 1998, Tagungsband, herausgegeben vom Lehrstuhl für Mathematik und ihre Didaktik der Universität Bayreuth, 1999.

Lempio, Frank:

Set-Valued Interpolation, Differential Inclusions, and Sensitivity in Optimization,
in: R. Lucchetti and J. Revalski (eds.): Recent Developments in Well-Posed Variational Problems, Mathematics and its Applications 331, Dordrecht: Kluwer Academic Publishers, 1995, pp. 137-169.

Lempio, Frank:

Über zwei Jahrtausende Finite Elemente - von Eudoxos bis zur Hyperthermietherapie,
Bayreuther Mathematische Schriften 56 (1999), pp. 59-78.

Lempio, Frank:

Difference Methods for Monotone Differential Inclusions,
in: A. Karmann, K. Mosler, M. Schader and G. Uebe (eds.): Operations Research '92, Extended Abstracts of the 17th Symposium on Operations Research held at the Universität der Bundeswehr Hamburg August 25-28, 1992, Heidelberg: Physika-Verlag, 1992, pp. 235-236.

Lempio, Frank:

Difference methods for differential inclusions,
Lecture Notes in Economics and Mathematical Systems, Vol. 378, 1992, pp. 236-273.

Lempio, Frank:

Euler's Method Revisited,
Proceedings of Steklov Institute of Mathematics, Moscow, Vol. 211, 1995, pp. 473-494.

Lempio, Frank:

Finite Element Methods - From Ancient to Modern Times
(in Bulgarian),
in: Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences (ed.), Proceedings of Twenty Ninth Spring Conference of the Union of Bulgarian Mathematicians, Lovetch, April 3-6, 2000, pp. 5-17.

Lempio, Frank:

Modified Euler Methods for Differential Inclusions,
in: A. B. Kurzhanski and V. M. Veliov (eds.): Set-Valued Analysis and Differential Inclusions, A Collection of Papers resulting from a Workshop held in Pamporovo, Bulgaria, September 17-21, 1990, Boston-Basel-Berlin: Birkhäuser-Verlag, 1993, pp. 131-148.

Lempio, Frank:

The Numerical Treatment of Differential Inclusions
in: P. Popivanov and S. Tersian (eds.): Proceedings of the International Conference on Differential Equations and Applications, held in Rousse, Bulgaria, August 13-19, 1989, Rousse: Technical University-Rousse Centre of Mathematics, 1991, pp. 353-364.

Pesch, Hans Josef and Gerdts, Matthias:

Simulation of Test-drives of Automobiles at Driving Limit,
in: W. Jäger, H.-J. Krebs (Eds.), 'Mathematics-Key Technology for the Future', pp. 74-83, Springer, 2003.

Rathmann, Wigand:

Modellierung, Simulation und Steuerung von Netzwerken schwingender Balken mittels dynamischer Bereichszerlegung,
Bayreuther Mathematische Schriften 60 (2000).

Schittkowski, Klaus und Zillober, Christian:

Sequential convex programming methods,
Proceedings of the 2nd GAMM/IFIP-workshop on stochastic optimization: numerical methods and technical applications, Munich, June 15-17, 1993, edited by K. Marti et al. Lecture Notes in Economics and Mathematical Systems 423, pp. 123-141, 1995.

Schittkowski, Klaus, Zillober, Christian und Zotemantel, Rainer:

Numerical Comparison of Nonlinear Programming Algorithms for Structural Optimization,
Structural Optimization, Vol. 7, No. 1 (1994), 1-28.

Schittkowski, Klaus:

Solving Nonlinear Programming Problems with very many Constraints,
Optimization, Vol. 25 (1992), 179-196.

Schittkowski, Klaus:

Some Experiments on Heuristic Code Selection Versus Numerical Performance in Nonlinear Programming,
European Journal of Operational Research, Vol. 65, No. 3 (1993), 292-305.

Zillober, Christian und Vogel, Frank:

Adaptive strategies for large scale optimization problems in mechanical engineering,
in: Recent Advances in Applied and Theoretical Mathematics, edited by N. Mastorakis, pp. 156-161.

Zillober, Christian und Vogel, Frank:

Solving large scale structural optimization problems,
Proceedings of the 2^nd ASMO UK/ISSMO conference on Engineering Design Optimization, Swansea, July 10-11, 2000, pp. 273-280, edited by J. Sienz.

Zillober, Christian:

A Globally Convergent Version of the Method of Moving Asymptotes,
Structural Optimization, Vol. 6, (1993), 166-174.

Zillober, Christian:

Software manual for SCPIP 2.2,
Technical Report Nr. TR01-2, Informatik, Universität Bayreuth, 2001.

Zillober, Christian:

A combined convex approximation - interior point approach for large scale Nonlinear Programming,
Optimization and Engineering, Vol. 2, pp. 51-73, 2001.

Zillober, Christian:

Convex approximation methods for practical optimization,
Operations Research Proceedings 2000, edited by B. Fleischmann et al., Springer Verlag, Berlin, Heidelberg, pp. 20-25, 2001.

Zillober, Christian:

Global convergence of a Nonlinear Programming method using convex approximations,
Numerical Algorithms, Vol. 27, pp. 256-289, 2001.

Zillober, Christian:

SCP - an Implementation of a Sequential Convex Programming Algorithm,
Schwerpunktprogramm der DFG 'Anwendungsbezogene Optimierung und Steuerung', Rep.470, 1993.

Zillober, Christian:

Stable computation of interior point solutions for a class of nonlinear convex programming problems,
Advanced Modeling and Optimization, Vol. 2, pp. 53-69, 2000.