KIT - IOR - KOP - Mitarbeiter

Sprechzeiten

in der Vorlesungszeit:
Donnerstag 10:00 Uhr bis 11:00 Uhr

in der vorlesungsfreien Zeit:
nur nach Vereinbarung

Forschungsinteressen

Optimierungsverfahren und ihre theoretischen Grundlagen
Robuste und Semi-infinite Optimierung
Verallgemeinerte Nash-Spiele
Parametrische Optimierung
Gemischt-ganzzahlige nichtlineare Optimierung
Partielle Differentialgleichungen und Kontrolltheorie
Data Envelopment Analysis

Publikationen

Wissenschaftliche Veröffentlichungen

Herausgebertätigkeiten für folgende Zeitschriften:

Journal of Global Optimization (Mitglied des Editorial-Boards).
Mathematical Methods of Operations Research (Mitglied des Editorial-Boards).
Optimization (Mitglied des Editorial-Boards).
Central European Journal of Operations Research, Volume 16, Number 2 (2008) (Sonderband "Advances in Continuous Optimization", Gast-Herausgeber).
Mathematical Programming, Series B, Volume 136, Issue 1 (2012) (Ausgabe "Parametric Optimization - Recent Advances", Gast-Herausgeber)
Pacific Journal of Optimization (Sonderband "Equilibrium Optimization", Gast-Herausgeber, in Vorbereitung)
Bulletin of the Czech Econometric Society (Mitglied des Editorial-Boards).

Eingereicht zur Veröffentlichung:

P. Kirst, O. Stein, P. Steuermann, An enhanced spatial branch-and-bound method in global optimization with nonconvex constraints, IOR Preprint 2/2013, Karlsruhe Institute of Technology (KIT), March 2013.
N. Harms, C. Kanzow, O. Stein, Smoothness properties of a regularized gap function for quasi-variational inequalities, IOR Preprint 1/2013, Karlsruher Institut für Technologie (KIT), März 2013.

Veröffentlichungen in Zeitschriften:

45		O. Stein, P. Steuermann, On smooth relaxations of obstacle sets, erscheint in: Optimization and Engineering.
44		O. Stein, Twice differentiable characterizations of convexity notions for functions on full dimensional convex sets, Schedae Informaticae, Vol. 21 (2012), 55-63.
43		N. Harms, C. Kanzow, O. Stein, On differentiability properties of player convex generalized Nash equilibrium problems, Optimization, iFirst.
42		O. Stein, How to solve a semi-infinite optimization problem, European Journal of Operational Research, Vol. 223 (2012), 312-320.
41		M. Diehl, B. Houska, O. Stein, P. Steuermann, A lifting method for generalized semi-infinite programs based on lower level Wolfe duality, Computational Optimization and Applications, Vol. 54 (2013), 189-210.
40		O. Stein, P. Steuermann, The adaptive convexification algorithm for semi-infinite programming with arbitrary index sets, Mathematical Programming, Ser. B, Vol. 136 (2012), 183-207.
39		V. Shikhman, O. Stein, On jet-convex functions and their tensor products, Optimization, Vol. 61 (2012), 717-731.
38		A. Dreves, C. Kanzow, O. Stein, Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems, Journal of Global Optimization, Vol. 53 (2012), 587-614.
37		D. Dorsch, V. Shikhman, O. Stein, Mathematical programs with vanishing constraints: critical point theory, Journal of Global Optimization, Vol. 52 (2012), 591-605.
36		D. Ralph, O. Stein, The C-index: a new stability concept for quadratic programs with complementarity constraints, Mathematics of Operations Research, Vol. 36 (2011), 504-526.
35		O. Stein, Lifting mathematical programs with complementarity constraints, Mathematical Programming, Vol. 131 (2012), 71-94.
34		O. Stein, A. Winterfeld, A feasible method for generalized semi-infinite programming, Journal of Optimization Theory and Applications, Vol. 146 (2010), 419-443.
33		O. Stein, A. Tezel, The semismooth approach for semi-infinite programming without strict complementarity, SIAM Journal on Optimization, Vol. 20 (2009), 1052-1072.
32		H. Günzel, H. Th. Jongen, O. Stein, Generalized semi-infinite programming: on generic local minimizers, Journal of Global Optimization, Vol. 42 (2008), 413-421.
31		V. Shikhman, O. Stein, Constrained optimization: projected gradient flows, Journal of Optimization Theory and Applications, Vol. 140 (2009), 117–130.
30		H. Th. Jongen, O. Stein, Smoothing by mollifiers. Part II: Nonlinear optimization, Journal of Global Optimization, Vol. 41 (2008), 335-350.
29		H. Th. Jongen, O. Stein, Smoothing by mollifiers. Part I: Semi-infinite optimization, Journal of Global Optimization, Vol. 41 (2008), 319-334.
28		H. Günzel, H. Th. Jongen, O. Stein, Generalized semi-infinite programming: the Symmetric Reduction Ansatz, Optimization Letters, Vol. 2 (2008), 415-424.
27		O. Stein, A. Tezel, The semismooth approach for semi-infinite programming under the Reduction Ansatz, Journal of Global Optimization, Vol. 41 (2008), 245-266.
26		H. Günzel, H. Th. Jongen, O. Stein, On the closure of the feasible set in generalized semi-infinite programming, Central European Journal of Operations Research, Vol. 15 (2007), 271-280.
25		C. A. Floudas, O. Stein, The adaptive convexification algorithm: a feasible point method for semi-infinite programming, SIAM Journal on Optimization, Vol. 18 (2007), 1187-1208.
24		S. D. Flåm, H. Th. Jongen, O. Stein, Slopes of shadow prices and Lagrange multipliers, Optimization Letters, Vol. 2 (2008), 143-155.
23		F. Guerra Vázquez, J.-J. Rückmann, O. Stein, G. Still, Generalized semi-infinite programming: a tutorial, Journal of Computational and Applied Mathematics, Vol. 217 (2008), 394-419.
22		J. Guddat, L. Neralic, O. Stein, Sensitivity analysis of the proportionate change of a subset of outputs or/and inputs in data envelopment analysis, Mathematical Communications, Vol. 11 (2006), 187-201.
21		O. Stein, On Karush-Kuhn-Tucker points for a smoothing method in semi-infinite optimization, Journal of Computational Mathematics, Vol. 24 (2006), 719-732.
20		O. Stein, M. Winkler, Amorphous molecular beam epitaxy: global solutions and absorbing sets, European Journal of Applied Mathematics, Vol. 16 (2005), 767-798.
19		O. Stein, J. Oldenburg, W. Marquardt, Continuous reformulations of discrete-continuous optimization problems, Computers and Chemical Engineering, Vol. 28 (2004), 1951-1966.
18		L. Neralic, O. Stein, On regular and parametric data envelopment analysis, Mathematical Methods of Operations Research, Vol. 60 (2004), 15-28.
17		O. Stein, On constraint qualifications in non-smooth optimization, Journal of Optimization Theory and Applications, Vol. 121 (2004), 647-671.
16		B. B. King, O. Stein, M. Winkler, A fourth order parabolic equation modeling epitaxial thin film growth, Journal of Mathematical Analysis and Applications, Vol. 286 (2003), 459-490.
15		H. Th. Jongen, O. Stein, On the complexity of equalizing inequalities, Journal of Global Optimization, Vol. 27 (2003), 367-374.
14		O. Stein, G. Still, Solving semi-infinite optimization problems with interior point techniques, SIAM Journal on Control and Optimization, Vol. 42 (2003), 769-788.
13		O. Stein, G. Still, On generalized semi-infinite optimization and bilevel optimization, European Journal of Operational Research, Vol. 142 (2002), 444-462.
12		H. Th. Jongen, O. Stein, Nonconvex optimization: gradient flows and deformation, Journal on Dynamical and Control Systems, Vol. 7 (2001), 425-446.
11		O. Stein, The role of the transition function in a continuum model for kinetic roughening and coarsening in thin films, Materials Science in Semiconductor Processing, Vol. 4 (2001), 405-416.
10		O. Stein, First order optimality conditions for degenerate index sets in generalized semi-infinite programming, Mathematics of Operations Research, Vol. 26 (2001), 565-582.
9		J.-J. Rückmann, O. Stein, On linear and linearized generalized semi-infinite optimization problems, Annals of Operations Research, Vol. 101 (2001), 191-208.
8		O. Stein, A note on the dual description of projected polytopes, Investigación Operacional, Vol. 22 (2001), 139-144.
7		A. Jess, H. Th. Jongen, L. Neralic, O. Stein, A semi-infinite programming model in data envelopment analysis, Optimization, Vol. 49 (2001), 369-385.
6		O. Stein, G. Still, On optimality conditions for generalized semi-infinite programming problems, Journal of Optimization Theory and Applications, Vol. 104 (2000), 443-458.
5		O. Stein, On level sets of marginal functions, Optimization, Vol. 48 (2000), 43-67.
4		H. Th. Jongen, O. Stein, On generic one-parametric semi-infinite optimization, SIAM Journal on Optimization, Vol. 7 (1997), 1103-1137.
3		H. Th. Jongen, J.-J. Rückmann, O. Stein, Generalized semi-infinite optimization: a first order optimality condition and examples, Mathematical Programming, Vol. 83 (1998), 145-158.
2		H. Th. Jongen, J.-J. Rückmann, O. Stein, Disjunctive optimization: critical point theory, Journal of Optimization Theory and Applications, Vol. 93 (1997), 321-336.
1		O. Stein, Bifurcations of hyperbolic fixed points for explicit Runge-Kutta methods, IMA Journal of Numerical Analysis, Vol. 17 (1997), 151-175.

Veröffentlichungen in referierten Tagungsbänden:

7		H. Th. Jongen, O. Stein, Constrained global optimization: adaptive gradient flows, in: C.A. Floudas, P.M. Pardalos (eds): Frontiers in Global Optimization, Kluwer Academic Publishers, Boston, 2004, 223-236.
6		J.-J. Rückmann, O. Stein, On convex lower level problems in generalized semi-infinite optimization, in: M.A. Goberna, M.A. Lopez (eds): Semi-Infinite Programming - Recent Advances, Kluwer, Dordrecht, 2001, 121-134.
5		O. Stein, The feasible set in generalized semi-infinite programming, in: M. Lassonde (ed): Approximation, Optimization and Mathematical Economics, Physica, Heidelberg, 2001, 309-327.
4		O. Stein, The Reduction Ansatz in absence of lower semi-continuity, in: J. Guddat, R. Hirabayashi, H.Th. Jongen, F. Twilt (eds): Parametric Optimization and Related Topics V, Peter Lang, Frankfurt a.M., 2000, 165-178.
3		O. Stein, Trap-doors in the solution set of semi-infinite optimization problems, in: P. Gritzmann, R. Horst, E. Sachs, R. Tichatschke (eds): Recent Advances in Optimization, Springer, Berlin, 1997, 348-355.
2		H. Th. Jongen, O. Stein, Parametric semi-infinite programming: jumps in the set of local minimizers, in: J. Guddat, H.Th. Jongen, F. Nozicka, G. Still, F. Twilt (eds): Parametric Optimization and Related Topics IV, Peter Lang, Frankfurt a.M., 1997, 161-175.
1		R. Hettich, H. Th. Jongen, O. Stein, On continuous deformations of semi-infinite optimization problems, in: M. Florenzano, J. Guddat, M. Jimenez, H.Th. Jongen, G. Lopez Lagomasino, F. Marcellan (eds): Approximation and Optimization in the Caribbean II, Peter Lang, Frankfurt a.M., 1995, 406-424.

Bücher und Skripten:

S. Nickel, O. Stein, K.-H. Waldmann, Operations Research, Springer, 2011.
O. Stein, Parametrische Optimierung, Karlsruher Institut für Technologie, 2011.
O. Stein, Globale Optimierung I und II, Karlsruher Institut für Technologie, 2011.
O. Stein, Nichtlineare Optimierung I und II, Karlsruher Institut für Technologie, 2012.
O. Stein, Parametrische Optimierung, FernUniversität in Hagen, 2004.
O. Stein, Bi-level Strategies in Semi-infinite Programming, Kluwer Academic Publishers, Boston, 2003.
O. Stein, On Parametric Semi-infinite Optimization, Shaker, Aachen, 1997.

Buchbeiträge:

O. Stein, Adaptive convexification in semi-infinite optimization, in: C.A. Floudas, P.M. Pardalos (eds): Encyclopedia of Optimization, Second Edition, Part 1, Springer, 2009, 13-19.
O. Stein, Continuous reformulations of discrete-continuous optimization problems, in: C.A. Floudas, P.M. Pardalos (eds): Encyclopedia of Optimization, Second Edition, Part 3, Springer, 2009, 493-501.
O. Stein, Generalized semi-infinite programming: optimality conditions, in: C.A. Floudas, P.M. Pardalos (eds): Encyclopedia of Optimization, Second Edition, Part 7, Springer, 2009, 1227-1233.
H. Th. Jongen, O. Stein, Smoothing methods for semi-infinite optimization, in: C.A. Floudas, P.M. Pardalos (eds): Encyclopedia of Optimization, Second Edition, Part 19, Springer, 2009, 3617-3622.
O. Stein, A semi-infinite approach to design centering, in: S. Dempe, V. Kalashnikov (eds): Optimization with Multivalued Mappings, Springer, 2006, 209-228.
H. Th. Jongen, J.-J. Rückmann, O. Stein, Parametric global optimization: sensitivity, in: C.A. Floudas, P.M. Pardalos (eds): Encyclopedia of Optimization, Vol. IV, Kluwer Academic Publishers, Dordrecht, 2001, 273-278.
H. Th. Jongen, O. Stein, Quasi-Newton methods, in: M. Hazewinkel (ed): Encyclopaedia of Mathematics, Supplement II, Kluwer Academic Publishers, Dordrecht, 2000, 396-398.

Sonstige Veröffentlichungen:

K.-H. Küfer, O. Stein, A. Winterfeld, Semi-infinite optimization meets industry: a deterministic approach to gemstone cutting, SIAM News, Vol. 41, No. 8 (2008), 1 und 16.
O. Stein, Ein Schnellkurs in Matlab, Manual, Lehrstuhl für Anwendungen des Operations Research, Universität Karlsruhe, 2006.
H. Th. Jongen, O. Stein, Optimierung: Eine Welt von Minima und Maxima, RWTH Themen, Vol. 2 (2001), 20-26.
J. A. Burns, B. B. King, O. Stein, Computational methods for identification and control of nanoscale materials, in: Proceedings of the 2000 MTNS (Mathematical Theory of Networks and Systems), June 19-23, Perpignan, France, 2000.
O. Stein, On epitaxial thin film growth and control of nanoscale materials, Report 00-04-01, ICAM, Virginia Tech, 2000.

Reviews:

Klicken Sie hier für eine Review-Liste von Oliver Stein (MathSciNet-Zugang erforderlich).

Bei Interesse an einem der nicht elektronisch verfügbaren Artikel senden Sie bitte Ihre vollständige Adresse an Prof. Dr. Oliver Stein .

Ausgewählte Vorträge

Inaugural lectures / Antrittsvorlesungen

18.01.12: Von generischen Optimierungsproblemen zu geschliffenen Edelsteinen, Inaugural Lecture, Faculty of Mathematics, KIT.
29.04.09: Brauchbare Antworten auf OR-Fragen, Inaugural Lecture, Faculty of Economics and Business Engineering, KIT.

Selected talks in the past five years

[ Conferences | Seminars and Colloquia ]

Talks in Conferences

20.08.12: On differentiability properties of player convex generalized Nash equilibrium problems, 21st International Symposium on Mathematical Programming, Berlin, August 19 - 24, 2012.
13.11.11: Plenary talk "The T-stationarity concept in nonsmooth optimization", 5th German Polish Conference on Optimization Methods and Applications, Krakow, Poland, November 9 - 13, 2011.
14.07.11: Solving MPCC feasibility problems as smooth systems of equations, IFORS 2011, Melbourne, Australia, July 10 - 15, 2011.
08.07.11: On jet-convex functions, 9th EUROPT Workshop on Advances in Continuous Optimization, Ballarat, Australia, July 8 - 9, 2011.
16.06.11: Solving nonlinear complementarity problems as smooth systems of equations, SIGOPT 2011, Lambrecht, June 15 - 17, 2011.
19.05.11: On the concept of T-stationarity in MPCC and MPVC, SIAM Conference on Optimization, Darmstadt, May 16 - 19, 2011.
10.02.11: On gemstones and maneuverability problems: applications of modern design centering techniques, Workshop on Advances in Nonlinear Optimization, Heidelberg, February 10, 2011.
02.09.10: Adaptive convexification for semi-infinite programs with arbitrary index sets, OR 2010, München, September 1 - 3, 2010.
14.06.10: Adaptive convexification for semi-infinite programs with arbitrary index sets, 4th Workshop on Optimization and Variational Analysis - in honor of Marco López, Elche, Spain, June 14 - 16, 2010.
24.08.09: Lifting mathematical programs with complementarity constraints, 20th International Symposium on Mathematical Programming, Chicago, USA, August 23 - 28, 2009.
07.07.09: Lifting mathematical programs with complementarity constraints, EURO XXIII, Bonn, July 5 - 8, 2009.
01.05.09: Lifting mathematical programs with complementarity constraints, 6th International Conference on Computational Management Science, Geneva, Switzerland, May 1 - 3, 2009.
04.09.08: The semismooth approach for semi-infinite programming without strict complementarity, OR 2008, Augsburg, September 3 - 5, 2008.
21.07.08: The semismooth approach for semi-infinite programming without strict complementarity, MOSOCOP 08 - Conference on Modeling, Simulation, and Optimization of Complex Processes, Heidelberg, July 21 -25, 2008.
18.02.08: Smoothing by mollifiers for finite and semi-infinite optimization problems, SIGOPT - International Conference on Optimization 2008, Lambrecht, February 18 - 21, 2008.
01.02.08: On gemstones and maneuverability problems: applications of modern design centering techniques, 29. OR-Südwestworkshop, Darmstadt, February 1, 2008.

Talks in Seminars and Colloquia

29.04.13: On differentiability properties of Nash equilibrium problems, Optimization and Applications Seminar, ETH Zürich and University of Zürich, Zürich, Switzerland.
19.03.13: On differentiability properties of Nash equilibrium problems, Mathematical Programming Seminar, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
18.01.13: On differentiability properties of Nash equilibrium problems, Kolloquium Mathematische Optimierung, University of Trier, Trier.
10.03.12: Die Geometrie der Optimierung und ihre Anwendung in den Wirtschaftswissenschaften, Tag der Mathematik, Karlsruhe Institute of Technology, Karlsruhe.
23.02.12: A lifting method for generalized semi-infinite programs based on lower level Wolfe duality, Mathematical Colloquium, Institute of Mathematics, Ilmenau University of Technology, Ilmenau.
28.05.10: Applications of modern design centering techniques, Oberseminar Optimierung, Julius-Maximilians-Universität Würzburg, Würzburg.
13.01.10: Liften von Optimierungsproblemen mit Komplementaritätsbedingungen, Dresdner Mathematisches Seminar, TU Dresden, Dresden.
02.06.09: Lifting mathematical programs with complementarity constraints, Mathematical Colloquium, University of Groningen, Groningen, The Netherlands.
16.04.09: Applications of modern design centering techniques, Mathematical Colloquium, Chemnitz University of Technology, Chemnitz.
30.03.09: Lifting mathematical programs with complementarity constraints, Optimisation and Numerical Analysis Seminar, University of Birmingham, Birmingham, United Kingdom.
02.06.08: On gemstones and maneuverability problems: applications of modern design centering techniques, CCES Seminar, RWTH Aachen University, Aachen.
28.02.08: On gemstones and maneuverability problems: applications of modern design centering techniques, OPTEC Seminar, Katholieke Universiteit Leuven, Leuven, Belgium.

Bisherige Lehrveranstaltungen

Bisherige Lehrveranstaltungen am Karlsruher Institut für Technologie:

Bitte wählen Sie Studium und Lehre.

Bisherige Lehrveranstaltungen außerhalb des Karlsruher Instituts für Technologie:

Wintersemester 2005/06 (an der Middle East Technical University Ankara)

Modern Concepts in Semi-infinite Optimization

Sommersemester 2005 (an der RWTH Aachen)

Vertiefung zur Vorlesung Analysis I/II (CAMPUS-Eintrag)
Übungen zur Analysis I/II (CAMPUS-Eintrag)

Wintersemester 2004/05 (an der Universität Duisburg-Essen)

Optimierung III (Nichtlineare Optimierung)
Übungen zur Optimierung III
Programmierseminar zur Optimierung III

Sommersemester 2004 (an der RWTH Aachen)

Proseminar Analysis (CAMPUS-Eintrag)
Übungen zur Optimierung A (CAMPUS-Eintrag)
Programmierübungen zur Optimierung A (CAMPUS-Eintrag)

Wintersemester 2003/04 (an der RWTH Aachen)

Ergänzungen zur Analysis I und II (CAMPUS-Eintrag)
Übungen zur Analysis III (CAMPUS-Eintrag)

Sommersemester 2003 (an der RWTH Aachen)

Analysis I (CAMPUS-Eintrag)
Übungen zur Analysis I (CAMPUS-Eintrag)
Übungen zur Analysis II (CAMPUS-Eintrag)

Wintersemester 2002/03 (an der RWTH Aachen)

Theorie der optimalen Steuerung (CAMPUS-Eintrag)
Übungen zur Analysis I (CAMPUS-Eintrag)

Sommersemester 2002 (an der TU Chemnitz)

Mathematik II (Teil 2) (für Elektro- und Informationstechniker)
Parametrische Optimierung

Lebenslauf

Professional Experience:	10/10 -	Co-opted member of the Faculty of Mathematics, KIT
	07/10 -	Lecturer at the KIT School of Energy
	10/08 -	Vice dean of education at the Faculty of Economics and Business Engineering
	09/08 -	Lecturer at the Hector School for Engineering and Management
	11/06 -	Full Professor at the Karlsruhe Institute of Technology
	07/05 - 11/06:	Heisenberg fellow of the German Research Foundation (DFG)
	02/06 - 04/06:	Academic Visitor at the Department of Chemical Engineering, Princeton University, USA
	07/05 - 09/05:	Academic Visitor at the Judge Business School, University of Cambridge, UK
	04/05 - 06/05:	Assistant Professor at RWTH Aachen University
	10/04 - 03/05:	Full Professor (substituting) at the University of Duisburg-Essen
	10/02 - 09/04:	Assistant Professor at RWTH Aachen University
	04/02 - 09/02:	Full Professor (substituting) at the Chemnitz University of Technology
	04/00 - 03/02:	Assistant Professor at RWTH Aachen University
	04/99 - 04/00:	Postdoc at the Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg VA, USA
		and fellowship holder of the Alexander von Humboldt-Stiftung
	07/97 - 03/99:	Assistant Professor at RWTH Aachen University
	01/97 - 06/97:	Wissenschaftlicher Angestellter at RWTH Aachen University
	04/95 - 12/96:	Member and scholarship holder of the "Graduiertenkolleg Mathematische Optimierung" at the University of Trier
	03/94 - 12/94:	Teaching Assistant at the University of Trier

Education and degrees:	07/02:	Habilitation at RWTH Aachen University, Venia Legendi for Mathematics
		Habilitation Thesis: Bi-level Strategies in Semi-infinite Programming
	01/97:	Graduation "mit Auszeichnung" (summa cum laude)
		Advisors: Prof. Dr. R. Hettich, University of Trier,
		and Prof. Dr. H. Th. Jongen, RWTH Aachen University
		Doctoral Thesis: On parametric semi-infinite optimization
		12/93: Diploma in mathematics (C/G numerical analysis) and economics at the University of Trier, Germany

Grants and awards:	11/2011:	KIT faculty teaching award
	07/05 - 11/06:	Heisenberg fellowship of the Deutsche Forschungsgemeinschaft
	04/99 - 04/00:	Feodor Lynen fellowship of the Alexander von Humboldt-Stiftung
	04/90 - 09/93:	Scholarship of the Friedrich Ebert-Stiftung

Professional Societies:		DMV, GAMM, GOR, MOS, SIAM, SIGOPT
		Member of several conference program and organization committees

Other Professional Activities:	94 - 96:	Mathematical consultant at the "Institut für Arbeitsrecht und Arbeitsbeziehungen in der Europäischen Gemeinschaft (IAAEG)", Trier
	89 - 94:	Freelancer at the news agency "Associated Press", Frankfurt a.M.

	Prof. Dr. Oliver Stein
	Leiter des Lehrstuhls Raum: 104 Tel.: +49 721 608-46782 Fax: +49 721 608-45440 steinVac4∂kit edu	Gebäude 20.13 1. OG