| Uni Graz | | me | | Home | | Home |Doz. Dr. Stefan Volkwein

Institut fr Mathematik und Wissenschaftlichen Rechnen
Karl-Franzens-Universität Graz
Heinrichstrasse 36
A-8010 Graz, Austria
e-mail: stefan.volkwein@uni-graz.at


Master Thesis

    Numerische Behandlung von absorbierenden Randbedingungen für hyperbolische Systeme (file name: diplom.ps, 17,56 Mega Byte), Department of Mathematics, University of Technology in Berlin, 1993.

PhD Thesis

    Mesh-independence of an augmented Lagrangian-SQP method in Hilbert spaces and control problems for the Burgers equation (file name: diss.ps, 4,44 Mega Byte), Department of Mathematics, University of Technology in Berlin, 1997.

Habilitationsschrift

    Optimal and suboptimal control of partial differential equations: augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition (file name: volkwein_habil.pdf), Institute of Mathematics, University of Graz, 2001.

Referred journal articles

    [1] S. Volkwein and A. Hepberger, Impedance Identification by POD Model Reduction Techniques. at-Automatisierungstechnik, 8:437-446, 2008.

    [2] F. Tröltzsch and S. Volkwein, POD a-posteriori error estimates for linear-quadratic optimal control problems. To appear in Computational Optimization and Applications.

    [3] M. Hintermüller, I. Kopacka, and S. Volkwein, Mesh-independence and preconditioning for solving control problems with mixed control-state constraints. To appear in ESAIM: Control, Optimisation and Calculus of Variations.

    [4] M. Mutsaers, M. Bachar, J. Batzel, F. Kappel, and S. Volkwein, Receding horizon controller for the baroreceptor loop in a model for the cardiovascular system. Cardiovascular Engineering, 8:14-22, 2008.

    [5] A. Borzi, J. Salomon, and S. Volkwein, Cascadic non-linear conjugate gradient solution to finite-level quantum optimal control problems. Journal of Computational and Applied Mathematics, 216:170-197, 2008.

    [6] K. Kunisch and S. Volkwein, Proper orthogonal decomposition for optimality systems. ESAIM: Mathemematical Modelling and Numerical Analysis, 42, 1-23, 2008.

    [7] B. Düring, A. Jüngel, and S. Volkwein, A sequential quadratic programming method for volatility estimation in option pricing. Journal on Optimization Theory and Applications, 38, August 2008.

    [8] M. Hinze and S. Volkwein, Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition. Computational Optimization and Applications, 39:319-345, 2008.

    [9] A. Unterreiter and S. Volkwein, Optimal control of the stationary quantum drift-diffusion model. Communications in Mathematical Sciences, 5:85-111, 2007.

    [10] T. Gänzler, S. Volkwein, and M. Weiser, SQP methods for parameter identification problems arising in hyperthermia. Optimization Methods and Software, 21:869-887, 2006.

    [11] F. Leibfritz and S. Volkwein, Reduced order output feedback control design for PDE systems using proper orthogonal decomposition and nonlinear semidefinite programming. Linear Algebra and Its Applications, 415:542-757, 2006. Abstract

    [12] M. Hinze and S. Volkwein, Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: error estimates and suboptimal control. In Reduction of Large-Scale Systems, P. Benner, V. Mehrmann, D. C. Sorensen (eds.), Lecture Notes in Computational Science and Engineering, Vol. 45, 261-306, 2005.

    [13] R. Griesse and S. Volkwein, A primal-dual active set strategy for optimal boundary control of a nonlinear reaction-diffusion system. SIAM Journal on Control and Optimization, 44:467-494, 2005. Abstract

    [14] K. Kunisch, S. Volkwein, and L. Xie, HJB-POD based feedback design for the optimal control of evolution problems. SIAM Journal on Applied Dynamical Systems, 3:701-722, 2004. Abstract

    [15] J. Wimmer, F. Kappel, S. Volkwein, B. Haditsch, H. Holzer, and D. Schneditz, On-line identification of hemodynamic variables by dilution off ultra-pure dialysate during hemodialysis. Cardiovascular Engineering, 4:39-46, 2004. Abstract

    [16] M. Hintermüller, K. Kunisch, Y. Spasov, and S. Volkwein, Dynamical system based optimal control of incompressible fluids. International Journal for Numerical Methods in Fluids, 46:345-359, 2004.

    [17] S. Volkwein, Nonlinear conjugate gradient methods for the optimal control of laser surface hardening. Optimization Methods and Software, 18:179-199, 2004. Abstract

    [18] D. Hömberg and S. Volkwein, Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition. Mathematical and Computer Modeling, 38:1003-1028, 2003. Abstract

    [19] S. Volkwein, Lagrange-SQP techniques for the control constrained optimal boundary control problems for the Burgers equation. Computational Optimization and Applications, 26:253-284, 2003. Abstract

    [20] S. Volkwein and M. Weiser, Affine invariant convergence analysis for inexact augmented Lagrangian-SQP mehods. SIAM Journal on Control and Optimization, 41:875-899, 2002. Abstract

    [21] K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM Journal on Numerical Analysis, 40:492-515, 2002. Abstract

    [22] E. Sachs and S. Volkwein, Augmented Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates. SIAM Journal on Numerical Analysis, 40:233-253, 2002. Abstract

    [23] S. Volkwein, Mesh-independence of Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates. Optimization Methods and Software, 17:77-111, 2002. Abstract

    [24] M. Hinze and S. Volkwein, Analysis of instantaneous control for the Burgers equation. Nonlinear Analysis -- Theory and Methods and Applications, 50:1-26, 2002. Abstract

    [25] S. Volkwein, Second-order conditions for boundary control problems of the Burgers equation. Control and Cybernetics, 30:249-278, 2001. Abstract

    [26] K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for parabolic problems. Numerische Mathematik, 90:117-148, 2001. Abstract

    [27] F. Tröltzsch and S. Volkwein, The SQP method for control constrained optimal control of the Burgers equation. ESAIM: Control, Optimisation and Calculus of Variations, 6:649-674, 2001. Abstract

    [28] S. Volkwein, Distributed control problems for the Burgers equation. Computational Optimization and Applications, 18:133-158, 2001. Abstract

    [29] S. Volkwein, Optimal control of a phase-field model using proper orthogonal decomposition. Zeitschrift für Angewandte Mathematik und Mechanik, 81:83-97, 2001. Abstract

    [30] S. Volkwein, Mesh-independence for an augmented Lagrangian-SQP method in Hilbert spaces. SIAM Journal on Control and Optimization, 38:767-785, 2000. Abstract

    [31] S. Volkwein, Application of the augmented Lagrangian-SQP method to optimal control problems for the stationary Burgers equation. Computational Optimization and Applications, 16:57-81, 2000. Abstract

    [32] K. Kunisch and S. Volkwein, Control of Burgers' equation by a reduced order approach using proper orthogonal decomposition. Journal on Optimization Theory and Applications, 102:345-371, 1999. Abstract

Referred proceeding articles

    [1] M. Kahlbacher and S. Volkwein, Estimation of regularization parameters in elliptic optimal control problems by POD model reduction, in Proceedings of the IFIP conference in Crakow (to appear).

    [2] K. Prenninger, W. Hirschberg and S. Volkwein, Objective Vehicle Dynamics Evaluation of Heavy Commercial Vehicles by means of Model based Parameter Identifcation, in: FISITA 2008, World Automotive Congress, Munich, Germany, 2008 (to appear).

    [3] M. Kahlbacher and S. Volkwein, Estimation of diffusion coefficients in a scalar Ginzburg-Landau equation by using model reduction. Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007, Kunisch, Karl; Of, Günther; Steinbach, Olaf (Eds.), Springer-Verlag, Heidelberg, 727-734, 2008.

    [4] W. Rosinger, S. Eitzinger, W. Hirschberg and S. Volkwein, Entwurf eines Sollwertgenerators für Fahrdynamikregelsysteme, erschienen in den Proceedings zum 15. Steierisches Seminar für Regelungstechnik und Prozessautomatisierung, Schloss Retzhof, 2007.

    [5] K. Prenninger, W. Hirschberg and S. Volkwein, A novel approach in vehicle dynamics. Parameter estimation of the non-linear sideslip stiffness, VDI-Berichte 1990, Erprobung und Simulation in der Fahrzeugentwicklung, (ISBN 978-3-18-091990-4), 13. VDI-Fachtagung, Würzburg, VDI Verlag GmbH, Düsseldorf, 359-374, 2007

    [6] M. Kahlbacher and S. Volkwein, Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems. Discussiones Mathematicae: Differential Inclusions, Control and Optimization, 27:95-117, 2007.

    [7] S. Brandl, I. Hauer, H.-H. Priebsch, T. Bartosch and S. Volkwein, Analysis and assessment of the sensitivity of trim parameters on SEA simulations for interior noise reduction. Proceedings of the 13th International Congress on Sound and Vibration (ICSV), Vienna, Austria, 2006.

    [8] S. Volkwein and S. Weiland, An algorithm for Galerkin projections in both time and spatial coordinates. Proceedings of the Seventeenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, July 24-28, 2006.

    [9] A. Hepberger, S. Volkwein, F. Diwoky, and H.-H. Priebsch, Impedance identification out of pressure datas with a hybrid measurement-simulation methodology up to 1kHz. In Proceedings of International Conference on Noise and Vibration Engineering, Leuven, Belgium, 2006.

    [10] H. Müller and S. Volkwein, Model reduction by proper orthogonal decomposition for lambda-omega systems. In Proceedings of European Conference on Computational Fluid Dynamics (ECCOMAS CFD), P. Wesseling, E. Onate, and J. Periaux (eds.), Egmont aan Zee, 2006.

    [11] M. Kahlbacher and S. Volkwein, Model reduction by proper orthogonal decomposition for estimation of scalar parameters in elliptic PDEs. In Proceedings of European Conference on Computational Fluid Dynamics (ECCOMAS CFD), P. Wesseling, E. Onate, and J. Periaux (eds.), Egmont aan Zee, 2006.

    [12] M. Hintermüller, S. Volkwein, and F. Diwoky, Fast solution techniques in constrained optimal boundary control of the semilinear heat equation. International Series of Numerical Mathematics, 155:119-147, 2007.

    [13] R. Griesse and S. Volkwein, Parametric Sensitivity Analysis for Optimal Boundary Control of a 3D Reaction-Diffusion System. Large-Scale Nonlinear Optimization. Series Nonconvex Optimization and Its Applications, Di Pillo and M. Roma (eds), Springer-Verlag, Berlin, 83:127-149, 2006.

    [14] F. Leibfritz and S. Volkwein, Numerical feedback controller design for PDE systems using model reduction: techniques and case studies. L. Biegler and O. Ghattas and M. Heinkenschloss and D. Keyes and B. van Bloemen Waanders (eds.), Real-Time PDE-Constrained Optimization, SIAM, 2006.

    [15] S. Volkwein, Condition number of the stiffness matrices arising in POD Galerkin schemes for dynamical systems. PAMM Proc. Appl. Math. Mech., 4, 39-42, 2004. Abstract

    [16] D. Hömberg, S. Volkwein, and W. Wolf, Optimal control strategies for the surface hardening of steel. 2nd International Conference on Thermal Process Modelling and Computer Simulation Nancy, France, March 31 - April 2, 2003, Journal de Physique IV (Proceedings), S. Denis, P. Archambault, J.-M. Bergheau, R. Fortunier (eds.), 120:325-335, 2004.

    [17] R. Griesse and S. Volkwein, A semi-smooth Newton method for optimal boundary control of a nonlinear reaction-diffusion system. Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Leuven, Belgium, July 5-9, 2004. Abstract

    [18] S. Volkwein, Interpretation of proper orthogonal decomposition as singular value decomposition and HJB-based feedback design. Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Leuven, Belgium, July 5-9, 2004. Abstract

    [19] D. Hömberg and S. Volkwein, Laser surface hardening using proper orthogonal decomposition for a three-dimensional example. PAMM Proc. Appl. Math. Mech., 3, 1-4, 2003. Abstract

    [20] K. Kunisch and S. Volkwein, Crank-Nicolson Galerkin Proper Orthogonal Decomposition Approximations for a General Equation in Fluid Dynamics. 18th GAMM Seminar on Multigrid and related methods for optimization problems, Leipzig, 97-114, 2002. Abstract

    [21] S. Volkwein, Boundary control of the Burgers equation: optimality conditions and reduced-order approach. In K.-H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels, and F. Tröltzsch, editors, Optimal Control of Complex Structures, International Series of Numerical Mathematics, 139:267-278, 2001. Abstract

    [22] F. Diwoky and S. Volkwein, Nonlinear boundary control for the heat equation utilizing proper orthogonal decomposition. In K.-H. Hoffmann, R. H. W. Hoppe, V. Schulz, editors, Fast Solution of Discretized Optimization Problems, International Series of Numerical Mathematics, 138:73-87, 2001. Abstract

    [23] K. Kunisch and S. Volkwein, Augmented Lagrangian-SQP techniques and their approximations. In S. Cox and I. Lasiecka, editors, Optimization Methods in Partial Differential Equations, volume 209 of Contemporary Mathematics, pages 147-159, 1997. Abstract

Technical report

    [1] M. Hintermüller and S. Volkwein, Primal-dual active set Methods for optimal control problems with mixed control-state and bilateral control constraints. Technical Report IMA04-07, University of Graz, 2007.

    [2] M. Hintermüller, H. Müller, and S. Volkwein, A semismooth Newton method for semilinear optimal control problems with control-state and integral-state constraints. Technical Report IMA03-07, University of Graz, 2007.

    [3] J. Wimmer, D, Schneditz, and S. Volkwein, A quasi-Newton method for robust identification of hemodynamic variables from indicator dilution curves. Technical Report, University of Graz, 2004.

    [4] S. Volkwein and M. Weiser, Optimality condition for a constrained parameter identification problem in hyperthermia. SFB-Preprint, 2004. Abstract

    [5] R. Griesse and S. Volkwein, Analysis for optimal boundary control for a three-dimensional reaction-diffusion system. SFB-Preprint, 2003. PDF-file

    [6] S. Volkwein, Bounds for condition numbers of mass and stiffness matrices arising in POD Galerkin approximations. SFB-Preprint, No. 283 2003. PDF-file

    [7] S. Volkwein, Upwind techniques and mixed finite elements for the steady-state Burgers equation. SFB-Preprint No. 278, 2003. PDF-file

    [8] S. Volkwein, Some remarks on augmented Lagrange-Newton SQP methods. SFB-Preprint No. 256, 2003. PDF-file

    [9] S. Volkwein, Optimal control of laser surface hardening by utilizing a nonlinear primal-dual active set strategy. SFB-Preprint No. 277, 2003. Abstract

    [10] S. Volkwein, A globalized SQP method for the optimal control of laser surface hardening. SFB-Preprint No. 272, 2003. Abstract

    [11] D. Hömberg and S. Volkwein, Suboptimal control of laser surface hardening using proper orthogonal decomposition. SFB-Preprint No. 217, 2001. PS-file

    [12] S. Volkwein, Proper orthogonal decomposition and singular value decomposition. SFB-Preprint No. 153, 1999. PS-file

Submitted

    [1] G. Scharrer, S. Volkwein, and T. Heubrandtner,Mathematical optimization of a plate volume under a p-Laplace PDE constraint by using standard software. Submitted, 2009.

    [2] G. von Winckel, A. Borzi, and S. Volkwein, A globalized Newton method for the accurate solution of a dipole quantum control problem. Submitted, 2009.

    [3] T. Tonn, K. Urban, and S. Volkwein, Optimal control of parameter-dependent convection-diffusion problems around rigid bodies. Submitted, 2008.

    [4] K. Kunisch and S. Volkwein, Optimal snapshot location for computing POD basis functions. Submitted, 2008.

Scripts

    [1] S. Volkwein, Proper Orthogonal Decomposition: Applications in Optimization and Control. Lecture Notes, CEA-EDF-INRIA Summer School Numerical Analysis Summer School Model Reduction and Reduced Basis methods: Application in Optimization. Saint-Lambert-des-Bois, Frankreich, Juni 23 to Juli 4, 2008, 74 pages, 2008, available as a PDF-file.

    [2] S. Volkwein, Model Reduction using Proper Orthogonal Decomposition. Script in English language, 42 pages, 2008, available as a PDF-file.

    [3] S. Volkwein, Numerische Verfahren der restringierten Optimierung. Script in German language, 90 pages, 2009, available as a PDF-file.

    [4] S. Volkwein, Basic functional analysis for the optimization of partial differential equations. Script in English language, 31 pages, 2003, available as a PS-file and a PDF-file.

    [5] S. Volkwein, Grundlagen der Optimierung. Script in German language, 34 pages, 2002, available as a PS-file and a PDF-file.

Curriculum Vitae

    Curiculum Vitae (English version)

    Lebenslauf (Deutsche Version)


If you would be interested in a copy of an article, I am very pleased. Please, feel free and contact me per email.


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last changed: March 05, 2009