Books
- “Analysis, Deep Learning, and Connections to Optimization”, Springer, Cham, 2024 (181 pages).
- “Vector Optimization – Theory, Applications, and Extensions”, Springer, Berlin (first edition: 2004, 465 pages; second edition: 2011, 481 pages).
- “Introduction to the Theory of Nonlinear Optimization”, Springer, Berlin (first edition: 1994, 249 pages; second edition: 1996, 257 pages; third edition: 2007, 292 pages), Springer, Cham (fourth edition: 2020, 323 pages).
- “Aufgabensammlung zur Ingenieurmathematik”, Shaker, Aachen, 2006 (132 pages).
- (edited with W. Krabs) “Recent Advances and Historical Development of Vector Optimization”, Springer, Lecture Notes in Economics and Mathematical Systems No. 294, Berlin, 1987 (405 pages).
- “Mathematical Vector Optimization in Partially Ordered Linear Spaces”, Peter Lang, Frankfurt, 1986 (310 pages).
Edited journal issues
- (edited with A.A. Khan, T. Tanaka, and X.D.H. Truong) “Special Issue on Set-Valued Analysis, Vector and Set Optimization, and Variational Inequalities”, Minimax Theory and its Applications 9 (2024) 157-432.
- (edited with G.Y. Chen) “Special Issue on Set-Valued Optimization”, Mathematical Methods of Operations Research 48, Issue 2 (1998) 151–285.
- “Special Issue on Vector Optimization”, ZOR Methods and Models of Operations Research 35, Issue 3 (1991) 175–265.
Publications in peer-reviewed journals
- (with T.X.D. Ha) “Bishop-Phelps cones given by an equation in Banach spaces”, Optimization 72 (2023) 1309–1346.
- “A unified approach to Bishop-Phelps and scalarizing functionals”, Journal of Applied and Numerical Optimization 5 (2023) 5–25.
- “Characterizations of the set less order relation in nonconvex set optimization”, Journal of Optimization Theory and Applications 193 (2022) 523–544.
- “Vectorization in nonconvex set optimization”, Journal of Applied and Numerical Optimization 4 (2022) 19–36.
- (with A.A. Khan) “Optimality conditions in nonlinear vector optimization with variable ordering structures”, Pure and Applied Functional Analysis 6 (2021) 1317–1331.
- “Continuity of maximal value functionals in normed spaces”, Applied Set-Valued Analysis and Optimization 3 (2021) 317–323.
- (with G. Eichfelder) “Optimality conditions in discrete-continuous nonlinear optimization”, Minimax Theory and its Applications 6 (2021) 127–144.
- “General theorems of the alternative in variable ordering structures”, Journal of Nonlinear and Variational Analysis 5 (2021) 1–7.
- (with T.X.D. Ha) “Characterizations of strictly convex sets by the uniqueness of support points”, Optimization 68 (2019) 1321–1335.
- “A derivative-free rooted tree method in nonconvex set optimization”, Pure and Applied Functional Analysis 3 (2018) 603–623.
- (with M. Knossalla) “Lagrange theory of discrete-continuous nonlinear optimization”, Journal of Nonlinear and Variational Analysis 2 (2018) 317–342.
- (with J. Gräbner) “Optimization of the distribution of wind speeds using convexly combined Weibull densities”, Renewables: Wind, Water, and Solar (2017) 4:7.
- (with T.X.D. Ha) “Properties of Bishop-Phelps Cones”, Journal of Nonlinear and Convex Analysis 18 (2017) 415–429.
- “Karush-Kuhn-Tucker Conditions in Set Optimization”, Journal of Optimization Theory and Applications 172 (2017) 707–725.
- (with M. Bischoff and E. Köbis) “Hard uncertainties in multiobjective layout optimization of photovoltaic power plants”, Optimization 66 (2017) 361–380.
- (with M. Bischoff) “Economic objectives, uncertainties and decision making in the energy sector”, Journal of Business Economics 86 (2016) 85–102.
- “Vectorization in Set Optimization”, Journal of Optimization Theory and Applications 167 (2015) 783–795.
- “Directional derivative in set optimization with the set less order relation”, Taiwanese Journal of Mathematics 19 (2015) 737–757.
- “A derivative-free descent method in set optimization”, Computational Optimization and Applications 60 (2015) 393–411.
- (with S. Limmer and D. Fey) “GPU implementation of a multiobjective search algorithm”, Positivity 16 (2012) 397–404.
- (with T.X.D. Ha) “New Order Relations in Set Optimization”, Journal of Optimization Theory and Applications 148 (2011) 209–236.
- (with Q.H. Ansari) “T-epiderivatives of set-valued maps and its application to set optimization and generalized variational inequalities”, Taiwanese Journal of Mathematics 14 (2010) 2447–2468.
- (with E. Gebhardt) “Global solver for nonlinear bilevel vector optimization problems”, Pacific Journal of Optimization 5 (2009) 387–401.
- “Bishop-Phelps Cones in Optimization”, International Journal of Optimization: Theory, Methods and Applications 1 (2009) 123–139.
- (with G. Eichfelder) “Set-Semidefinite Optimization”, Journal of Convex Analysis 15 (2008) 767–801.
- “Multiobjective Search Algorithm with Subdivision Technique”, Computational Optimization and Applications 35 (2006) 161–175.
- (with C. Hillermeier) “Multiobjective optimization: survey of methods and industrial applications”, Surveys on Mathematics for Industry 11 (2005) 1–42.
- (with A.A. Khan and P. Zeilinger) “Second-Order Optimality Conditions in Set Optimization”, Journal of Optimization Theory and Applications 125 (2005) 331–347.
- (with A. Kirsch and C. Wagner) “Optimization of Rod Antennas of Mobile Phones”, Mathematical Methods of Operations Research 59 (2004) 37–51.
- (with A.A. Khan) “The Existence of Contingent Epiderivatives for Set-Valued Maps”, Applied Mathematics Letters 16 (2003) 1179–1185.
- (with L. Carosi and L. Martein) “On the connections between semidefinite optimization and vector optimization”, Journal of Interdisciplinary Mathematics 6 (2003) 219–229.
- (with A. Hutterer) “On the location of antennas for treatment planning in hyperthermia”, OR Spectrum 25 (2003) 397–412.
- (with A.A. Khan) “Some Calculus Rules for Contingent Epiderivatives”, Optimization 52 (2003) 113–125.
- (with A.A. Khan) “Existence theorems and characterizations of generalized contingent epiderivatives”, Journal of Nonlinear and Convex Analysis 3 (2002) 315–330.
- (with A.A. Khan) “Generalized contingent epiderivatives in set-valued optimization: optimality conditions”, Numerical Functional Analysis and Optimization 23 (2002) 807–831.
- (with S. Häßler) “Game-Theoretic Approach to the Optimization of FDDI Computer Networks”, Journal of Optimization Theory and Applications 106 (2000) 463–474.
- (with A. Götz) “The Lagrange Multiplier Rule in Set-Valued Optimization”, SIAM Journal on Optimization 10 (1999) 331–344.
- (with J. Baier) “On Subdifferentials of Set-Valued Maps”, Journal of Optimization Theory and Applications 100 (1999) 233–240.
- (with G.Y. Chen) “Optimality Conditions for Set-Valued Optimization Problems”, Mathematical Methods of Operations Research 48 (1998) 187–200.
- (with R. Rauh) “Contingent Epiderivatives and Set-Valued Optimization”, Mathematical Methods of Operations Research 46 (1997) 193–211.
- (with A. Jüschke and A. Kirsch) “A Bicriterial Optimization Problem of Antenna Design”, Computational Optimization and Applications 7 (1997) 261–276.
- “On the Determination of Minimal Facets and Edges of a Polyhedral Set”, Journal of Multi-Criteria Decision Analysis 6 (1997) 17–24.
- (with D.T. Luc) “Axiomatic Approach to Duality in Optimization”, Numerical Functional Analysis and Optimization 13 (1992) 305–326.
- (with A. Merkel) “Reference Point Approximation Method for the Solution of Bicriterial Nonlinear Optimization Problems”, Journal of Optimization Theory and Applications 74 (1992) 87–103.
- “A Generalization of a Theorem of Arrow, Barankin, and Blackwell”, SIAM Journal on Control and Optimization 26 (1988) 999–1005.
- “Parametric Approximation Problems Arising in Vector Optimization”, Journal of Optimization Theory and Applications 54 (1987) 503–516.
- “Existence Theorems in Vector Optimization”, Journal of Optimization Theory and Applications 50 (1986) 397–406.
- (with E. Sachs) “Generalized Quasiconvex Mappings and Vector Optimization”, SIAM Journal on Control and Optimization 24 (1986) 306–322.
- “A Characterization of Properly Minimal Elements of a Set”, SIAM Journal on Control and Optimization 23 (1985) 649–656.
- “Some Characterizations of the Optimal Solutions of a Vector Optimization Problem”, OR Spektrum 7 (1985) 7–17.
- “Scalarization in Vector Optimization”, Mathematical Programming 29 (1984) 203–218.
- “Zur vektoriellen linearen Tschebyscheff-Approximation”, Mathematische Operationsforschung und Statistik, Series Optimization 14 (1983) 577–591.
- “Duality in Vector Optimization”, Mathematical Programming 25 (1983) 343–353.
- “Ein Verfahren zur interaktiven Lösung nichtlinearer Vektoroptimierungsprobleme”, OR Spektrum 3 (1982) 239–243.
- “A Globally Convergent Method for Nonlinear Programming”, Mathematische Operationsforschung und Statistik, Series Optimization 12 (1981) 493–511.
- “Zur Bewertung von Schätzungen bei der gewöhnlichen Regressionsanalyse”, Metrika 28 (1981) 23–33.
- “An Interior Point Method for Nonlinear Programming”, Zeitschrift für Operations Research 23 (1979) 1–15.
Habilitation and doctoral thesis
- “Vektoroptimierung und deren Anwendung in der Approximations- und Steuerungstheorie” (habilitation thesis, TH Darmstadt, 1983).
- “Sequentieller Innerer-Punkt-Algorithmus zur Lösung nichtlinearer Optimierungsprobleme” (dissertation, TH Darmstadt, 1978).
Proceedings and book contributions
- (with G. Eichfelder) “Vector and Set Optimization”, in: S. Greco, M. Ehrgott and J.R. Figueira (eds.), Multiple Criteria Decision Analysis – State of the Art Surveys, Volume 2 (Springer, New York, 2016), Chapter 17, p. 695–737.
- (with G. Eichfelder) “Vector Optimization Problems and Their Solution Concepts”, in: Q.H. Ansari and J.-C. Yao (eds.), Recent Developments in Vector Optimization (Springer, Heidelberg, 2012), Chapter 1, p. 1–27.
- (with S. Liu, T. Fühner, F. Shao, A. Barenbaum and A. Erdmann) “Topography-aware BARC optimization for double patterning”, in: M.V. Dusa and W. Conley (eds.), Proceedings of the SPIE, Volume 7640 (2010) 76403C.
- (with G. Eichfelder) “Foundations of Set-Semidefinite Optimization”, in: P.M. Pardalos, T.M. Rassias and A.A. Khan (eds.), Nonlinear Analysis and Variational Problems (Springer, New York, 2010), Chapter 18, p. 259–284.
- (with K. Miettinen, K. Deb, W. Ogryczak, K. Shimoyama and R. Vetschera) “Future Challenges”, in: J. Branke, K. Deb, K. Miettinen and R. Slowinski (eds.), Multiobjective Optimization – Interactive and Evolutionary Approaches (Springer, Lecture Notes in Computer Science No. 5252, Berlin, 2008), p. 435–461.
- (with U. Rathje) “Graef-Younes Method with Backward Iteration”, in: K.-H. Küfer, H. Rommelfanger, C. Tammer and K. Winkler (eds.), Multicriteria Decision Making and Fuzzy Systems – Theory, Methods and Applications (Shaker Verlag, Aachen, 2006), p. 75–81.
- “Grundlagen der Mengenoptimierung”, in: W. Habenicht, B. Scheubrein and R. Scheubrein (eds.), Multi-Criteria- und Fuzzy-Systeme in Theorie und Praxis (DUV Gabler Edition Wissenschaft, Wiesbaden, 2003), p. 37–71.
- “Set-Valued Optimization”, in: C.A. Floudas and P.M. Pardalos (eds.), Encyclopedia of Optimization (first edition: Kluwer, 2001, p. 2352–2355; second edition: Springer, 2009, p. 3486–3488), third edition by P.M. Pardalos and O.A. Prokopyev, Springer, Cham, 2024, https://doi.org/10.1007/978-3-030-54621-2_600-1 .
- “Theory of Vector Maximization: Various Concepts of Efficient Solutions”, Chapter 2 in: T. Gal, T.J. Stewart and T. Hanne (eds.), Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications (Kluwer, Boston, 1999), p. 2-1 – 2-32.
- “Optimality Conditions in Set-Valued Vector Optimization”, in: G. Fandel and T. Gal (eds.), Multiple Criteria Decision Making – Proceedings of the Twelfth International Conference, Hagen (Germany) (Springer, Lecture Notes in Economics and Mathematical Systems No. 448, Berlin, 1997), p. 22–30.
- “Angewandte nichtlineare Vektoroptimierung”, Newsletter of GMÖOR 1/2 1995, p. 3–12.
- “On the Solution of Linear Vector Optimization Problems in the Image Space”, in: A. Bachem, U. Derigs, M. Jünger and R. Schrader (eds.), Operations Research ’93 (Physica, Heidelberg, 1994), p. 280–283.
- (with J. Klose and A. Merkel) “On the Application of a Method of Reference Point Approximation to Bicriterial Optimization Problems in Chemical Engineering”, in: W. Oettli and D. Pallaschke (eds.), Advances in Optimization – Proceedings, Lambrecht, FRG, 1991 (Springer, Lecture Notes in Economics and Mathematical Systems No. 382, Berlin, 1992), p. 478–491.
- “Vector Optimization: Theory, Methods, and Application to Design Problems in Engineering”, in: W. Krabs and J. Zowe (eds.), Modern Methods of Optimization – Proceedings, Bayreuth, FRG, October 1–6, 1990 (Springer, Lecture Notes in Economics and Mathematical Systems No. 378, Berlin, 1992), p. 127–150.
- “A Method of Reference Point Approximation in Vector Optimization”, in: H Schellhaas, P. van Beek, H. Isermann, R. Schmidt and M. Zijlstra (eds.), Operations Research Proceedings 1987 (Springer, Berlin, 1988), p. 576–587.
- (with W. Krabs) “Applications of Multicriteria Optimization in Approximation Theory”, in: W. Stadler (ed.), Multicriteria Optimization in Engineering and in the Sciences (Plenum Press, New York, 1988), p. 49–75.
- “Duality in Partially Ordered Sets”, in: J. Jahn and W. Krabs (eds.), Recent Advances and Historical Development of Vector Optimization (Springer, Lecture Notes in Economics and Mathematical Systems No. 177, Berlin, 1987), p. 160–172.
- “Problems of Vector Optimization”, Methods of Operations Research 57 (1987) 51–59.
- “Existenzsätze in der Vektoroptimierung”, in: G. Linnemann (ed.), 30. Internationales Wissenschaftliches Kolloquium 1985 (Issue 4, Technische Hochschule Ilmenau, 1985), p. 67–69.
- “Scalarization in Multi Objective Optimization”, in: P. Serafini (ed.), Mathematics of Multi Objective Optimization (Springer, Wien, 1985), p. 45–88.
- “Properly Minimal Elements of a Set”, in: C. Lemaréchal (ed.), Third Franco-German Conference in Optimization (INRIA Report, Rocquencourt, 1985), p. 27–28.
- “Neuere Entwicklungen in der Vektoroptimierung”, in: H. Steckhan, W. Bühler, K.-E. Jäger, Ch. Schneeweiß and J. Schwarze (eds.), Operations Research Proceedings 1983 (Springer, Berlin, 1984), p. 511–519.
- “Mathematical Applications of MCDM: Vector Approximation and Cooperative Differential Games”, in: P. Hansen (ed.), Essays and Surveys on Multiple Criteria Decision Making (Springer, Lecture Notes in Economics and Mathematical Systems No. 209, Berlin, 1983), p. 177–186.
- “Dualität in der Vektoroptimierung mit Anwendung in der vektoriellen Approximation”, in: G. Linnemann (ed.), 27. Internationales Wissenschaftliches Kolloquium 1982 (Issue 5, Technische Hochschule Ilmenau, 1982), p. 7–9.
- “The Haar Condition in Vector Optimization”, in: G. Fandel and T. Gal (eds.), Multiple Criteria Decision Making, Theory and Application (Springer, Lecture Notes in Economics and Mathematical Systems No. 177, Berlin, 1980), p. 128–134.
- “Lösung nichtlinearer Optimierungsprobleme mit Nebenbedingungen”, in: H. Späth (ed.), Ausgewählte Operations Research Software in FORTRAN (Oldenbourg, München, 1979), p. 30–50.
- (with R. Dupré and K. Huckert) “Lösung linearer Vektormaximumprobleme durch das STEM-Verfahren”, in: H. Späth (ed.), Ausgewählte Operations Research Software in FORTRAN (Oldenbourg, München, 1979), p. 9–29.
- “Zur Stabilität von Regressionskoeffizienten”, Operations Research Verfahren 33 (1979) 209–215.
- “Ein Algorithmus vom Typ der zulässigen Richtungen zur Lösung nichtlinearer Optimierungsprobleme mit Ungleichungsrestriktionen”, Operations Research Verfahren XXVIII (1978) 407–411.
Preprint
- (with F. Eibenstein and G. Leitmann) “On the Global Asymptotic Stabilization of Nonlinear Systems”, Preprint No. 838, Fachbereich Mathematik, TH Darmstadt (1984).
Online article
- “Nicht die Reichweite, sondern die Ladeinfrastruktur entscheidet”, SpringerProfessional, 12.12.2018 (link).
Patents
- (with D. Diehl, G. Eichfelder, M. Gebhardt, J. Gierling and D. Ritter) “RF-PULSE OPTIMIZATION FOR THE PARALLEL TRANSMISSION OF RF PULSES VIA A PLURALITY OF INDEPENDENT HIGH-FREQUENCY TRANSMISSION CHANNELS IN MAGNETIC RESONANCE”, European Patent Office, publication no. WO2012119673 (A1) (also DE102011005174 (A1) and US2012286778 (A1)), applicant: FAU Erlangen-Nürnberg and Siemens AG, 2011. Bibliographic data.
- (with A. Kirsch and C. Wagner) ”ROD ANTENNA FOR A MOBILE RADIO TELEPHONE”, European Patent Office, publication no. WO0156110 (A1), applicant: Siemens AG, 2001. Bibliographic data.