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List of Publications

Books

  1. “Vector Optimization – Theory, Applications, and Extensions”, Springer, Berlin (first edition: 2004, 465 pages; second edition: 2011, 481 pages).
  2. “Introduction to the Theory of Nonlinear Optimization”, Springer, Berlin (first edition: 1994, 249 pages; second edition: 1996, 257 pages; third edition: 2007, 292 pages).
  3. “Aufgabensammlung zur Ingenieurmathematik”, Shaker, Aachen, 2006 (132 pages).
  4. (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).
  5. “Mathematical Vector Optimization in Partially Ordered Linear Spaces”, Peter Lang, Frankfurt, 1986 (310 pages).

Edited journal issues

  1. (edited with G.Y. Chen) “Special Issue on ‘Set-Valued Optimization”, Mathematical Methods of Operations Research 48, Issue 2 (1998) 151–285.
  2. “Special Issue on Vector Optimization”, ZOR Methods and Models of Operations Research 35, Issue 3 (1991) 175–265.

Publications in peer-reviewed journals

  1. (with T.X.D. Ha) “Characterizations of strictly convex sets by the uniqueness of support points”, Optimization (to appear).
  2. “A derivative-free rooted tree method in nonconvex set optimization”, Pure and Applied Functional Analysis 3 (2018) 603–623.
  3. (with M. Knossalla) “Lagrange theory of discrete-continuous nonlinear optimization”, Journal of Nonlinear and Variational Analysis 2 (2018) 317–342.
  4. (with J. Gräbner) “Optimization of the distribution of wind speeds using convexly combined Weibull densities”, Renewables: Wind, Water, and Solar (2017) 4:7.
  5. (with T.X.D. Ha) “Properties of Bishop-Phelps Cones”, Journal of Nonlinear and Convex Analysis 18 (2017) 415–429.
  6. “Karush-Kuhn-Tucker Conditions in Set Optimization”, Journal of Optimization Theory and Applications 172 (2017) 707–725.
  7. (with M. Bischoff and E. Köbis) “Hard uncertainties in multiobjective layout optimization of photovoltaic power plants”, Optimization 66 (2017) 361–380.
  8. (with M. Bischoff) “Economic objectives, uncertainties and decision making in the energy sector”, Journal of Business Economics 86 (2016) 85–102.
  9. “Vectorization in Set Optimization”, Journal of Optimization Theory and Applications 167 (2015) 783–795.
  10. “Directional derivative in set optimization with the set less order relation”, Taiwanese Journal of Mathematics 19 (2015) 737–757.
  11. “A derivative-free descent method in set optimization”, Computational Optimization and Applications 60 (2015) 393–411.
  12. (with S. Limmer and D. Fey) “GPU implementation of a multiobjective search algorithm”, Positivity 16 (2012) 397–404.
  13. (with T.X.D. Ha) “New Order Relations in Set Optimization”, Journal of Optimization Theory and Applications 148 (2011) 209–236.
  14. (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.
  15. (with E. Gebhardt) “Global solver for nonlinear bilevel vector optimization problems”, Pacific Journal of Optimization 5 (2009) 387–401.
  16. “Bishop-Phelps Cones in Optimization”, International Journal of Optimization: Theory, Methods and Applications 1 (2009) 123–139.
  17. (with G. Eichfelder) “Set-Semidefinite Optimization”, Journal of Convex Analysis 15 (2008) 767–801.
  18. “Multiobjective Search Algorithm with Subdivision Technique”, Computational Optimization and Applications 35 (2006) 161–175.
  19. (with C. Hillermeier) “Multiobjective optimization: survey of methods and industrial applications”, Surveys on Mathematics for Industry 11 (2005) 1–42.
  20. (with A.A. Khan and P. Zeilinger) “Second-Order Optimality Conditions in Set Optimization”, Journal of Optimization Theory and Applications 125 (2005) 331–347.
  21. (with A. Kirsch and C. Wagner) “Optimization of Rod Antennas of Mobile Phones”, Mathematical Methods of Operations Research 59 (2004) 37–51.
  22. (with A.A. Khan) “The Existence of Contingent Epiderivatives for Set-Valued Maps”, Applied Mathematics Letters 16 (2003) 1179–1185.
  23. (with L. Carosi and L. Martein) “On the connections between semidefinite optimization and vector optimization”, Journal of Interdisciplinary Mathematics 6 (2003) 219–229.
  24. (with A. Hutterer) “On the location of antennas for treatment planning in hyperthermia”, OR Spectrum 25 (2003) 397–412.
  25. (with A.A. Khan) “Some Calculus Rules for Contingent Epiderivatives”, Optimization 52 (2003) 113–125.
  26. (with A.A. Khan) “Existence theorems and characterizations of generalized contingent epiderivatives”, Journal of Nonlinear and Convex Analysis 3 (2002) 315–330.
  27. (with A.A. Khan) “Generalized contingent epiderivatives in set-valued optimization: optimality conditions”, Numerical Functional Analysis and Optimization 23 (2002) 807–831.
  28. (with S. Häßler) “Game-Theoretic Approach to the Optimization of FDDI Computer Networks”, Journal of Optimization Theory and Applications 106 (2000) 463–474.
  29. (with A. Götz) “The Lagrange Multiplier Rule in Set-Valued Optimization”, SIAM Journal on Optimization 10 (1999) 331–344.
  30. (with J. Baier) “On Subdifferentials of Set-Valued Maps”, Journal of Optimization Theory and Applications 100 (1999) 233–240.
  31. (with G.Y. Chen) “Optimality Conditions for Set-Valued Optimization Problems”, Mathematical Methods of Operations Research 48 (1998) 187–200.
  32. (with R. Rauh) “Contingent Epiderivatives and Set-Valued Optimization”, Mathematical Methods of Operations Research 46 (1997) 193–211.
  33. (with A. Jüschke and A. Kirsch) “A Bicriterial Optimization Problem of Antenna Design”, Computational Optimization and Applications 7 (1997) 261–276.
  34. “On the Determination of Minimal Facets and Edges of a Polyhedral Set”, Journal of Multi-Criteria Decision Analysis 6 (1997) 17–24.
  35. (with D.T. Luc) “Axiomatic Approach to Duality in Optimization”, Numerical Functional Analysis and Optimization 13 (1992) 305–326.
  36. (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.
  37. “A Generalization of a Theorem of Arrow, Barankin, and Blackwell”, SIAM Journal on Control and Optimization 26 (1988) 999–1005.
  38. “Parametric Approximation Problems Arising in Vector Optimization”, Journal of Optimization Theory and Applications 54 (1987) 503–516.
  39. “Existence Theorems in Vector Optimization”, Journal of Optimization Theory and Applications 50 (1986) 397–406.
  40. (with E. Sachs) “Generalized Quasiconvex Mappings and Vector Optimization”, SIAM Journal on Control and Optimization 24 (1986) 306–322.
  41. “A Characterization of Properly Minimal Elements of a Set”, SIAM Journal on Control and Optimization 23 (1985) 649–656.
  42. “Some Characterizations of the Optimal Solutions of a Vector Optimization Problem”, OR Spektrum 7 (1985) 7–17.
  43. “Scalarization in Vector Optimization”, Mathematical Programming 29 (1984) 203–218.
  44. “Zur vektoriellen linearen Tschebyscheff-Approximation”, Mathematische Operationsforschung und Statistik, Series Optimization 14 (1983) 577–591.
  45. “Duality in Vector Optimization”, Mathematical Programming 25 (1983) 343–353.
  46. “Ein Verfahren zur interaktiven Lösung nichtlinearer Vektoroptimierungsprobleme”, OR Spektrum 3 (1982) 239–243.
  47. “A Globally Convergent Method for Nonlinear Programming”, Mathematische Operationsforschung und Statistik, Series Optimization 12 (1981) 493–511.
  48. “Zur Bewertung von Schätzungen bei der gewöhnlichen Regressionsanalyse”, Metrika 28 (1981) 23–33.
  49. “An Interior Point Method for Nonlinear Programming”, Zeitschrift für Operations Research 23 (1979) 1–15.

Habilitation and doctoral thesis

  1. “Vektoroptimierung und deren Anwendung in der Approximations- und Steuerungstheorie” (habilitation thesis, TH Darmstadt, 1983).
  2. “Sequentieller Innerer-Punkt-Algorithmus zur Lösung nichtlinearer Optimierungsprobleme” (dissertation, TH Darmstadt, 1978).

Proceedings and book contributions

  1. (with G. Eichfelder) “Vector and Set Optimization”, in: S. Greco, M. Ehrgott and J.R. Figueira (ed.), Multiple Criteria Decision Analysis – State of the Art Surveys, Volume 2 (Springer, New York, 2016), Chapter 17, p. 695–737.
  2. (with G. Eichfelder) “Vector Optimization Problems and Their Solution Concepts”, in: Q.H. Ansari and J.-C. Yao (ed.), Recent Developments in Vector Optimization (Springer, Heidelberg, 2012), Chapter 1, p. 1–27.
  3. (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 (ed.), Proceedings of the SPIE, Volume 7640 (2010) 76403C.
  4. (with G. Eichfelder) “Foundations of Set-Semidefinite Optimization”, in: P.M. Pardalos, T.M. Rassias and A.A. Khan (ed.), Nonlinear Analysis and Variational Problems (Springer, New York, 2010), Chapter 18, p. 259–284.
  5. (with K. Miettinen, K. Deb, W. Ogryczak, K. Shimoyama and R. Vetschera) “Future Challenges”, in: J. Branke, K. Deb, K. Miettinen and R. Slowinski (ed.), Multiobjective Optimization – Interactive and Evolutionary Approaches (Springer, Lecture Notes in Computer Science No. 5252, Berlin, 2008), p. 435–461.
  6. (with U. Rathje) “Graef-Younes Method with Backward Iteration”, in: K.-H. Küfer, H. Rommelfanger, C. Tammer and K. Winkler (ed.), Multicriteria Decision Making and Fuzzy Systems – Theory, Methods and Applications (Shaker Verlag, Aachen, 2006), p. 75–81.
  7. “Grundlagen der Mengenoptimierung”, in: W. Habenicht, B. Scheubrein and R. Scheubrein (ed.), Multi-Criteria- und Fuzzy-Systeme in Theorie und Praxis (DUV Gabler Edition Wissenschaft, Wiesbaden, 2003), p. 37–71.
  8. “Set-Valued Optimization”, in: C.A. Floudas and P.M. Pardalos (ed.), Encyclopedia of Optimization (first edition: Kluwer, 2001, p. 2352–2355; second edition: Springer, 2009, p. 3486–3488).
  9. “Theory of Vector Maximization: Various Concepts of Efficient Solutions”, Chapter 2 in: T. Gal, T.J. Stewart and T. Hanne (ed.), Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications (Kluwer, Boston, 1999), p. 2-1 – 2-32.
  10. “Optimality Conditions in Set-Valued Vector Optimization”, in: G. Fandel and T. Gal (ed.), 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.
  11. “Angewandte nichtlineare Vektoroptimierung”, Newsletter of GMÖOR 1/2 1995, p. 3–12.
  12. “On the Solution of Linear Vector Optimization Problems in the Image Space”, in: A. Bachem, U. Derigs, M. Jünger and R. Schrader (ed.), Operations Research ’93 (Physica, Heidelberg, 1994), p. 280–283.
  13. (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 (ed.), Advances in Optimization – Proceedings, Lambrecht, FRG, 1991 (Springer, Lecture Notes in Economics and Mathematical Systems No. 382, Berlin, 1992), p. 478–491.
  14. “Vector Optimization: Theory, Methods, and Application to Design Problems in Engineering”, in: W. Krabs and J. Zowe (ed.), 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.
  15. “A Method of Reference Point Approximation in Vector Optimization”, in: H Schellhaas, P. van Beek, H. Isermann, R. Schmidt and M. Zijlstra (ed.), Operations Research Proceedings 1987 (Springer, Berlin, 1988), p. 576–587.
  16. (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.
  17. “Duality in Partially Ordered Sets”, in: J. Jahn and W. Krabs (ed.), Recent Advances and Historical Development of Vector Optimization (Springer, Lecture Notes in Economics and Mathematical Systems No. 177, Berlin, 1987), p. 160–172.
  18. “Problems of Vector Optimization”, Methods of Operations Research 57 (1987) 51–59.
  19. “Existenzsätze in der Vektoroptimierung”, in: G. Linnemann (ed.), 30. Internationales Wissenschaftliches Kolloquium 1985 (Issue 4, Technische Hochschule Ilmenau, 1985), p. 67–69.
  20. “Scalarization in Multi Objective Optimization”, in: P. Serafini (ed.), Mathematics of Multi Objective Optimization (Springer, Wien, 1985), p. 45–88.
  21. “Properly Minimal Elements of a Set”, in: C. Lemaréchal (ed.), Third Franco-German Conference in Optimization (INRIA Report, Rocquencourt, 1985), p. 27–28.
  22. “Neuere Entwicklungen in der Vektoroptimierung”, in: H. Steckhan, W. Bühler, K.-E. Jäger, Ch. Schneeweiß and J. Schwarze (ed.), Operations Research Proceedings 1983 (Springer, Berlin, 1984), p. 511–519.
  23. “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.
  24. “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.
  25. “The Haar Condition in Vector Optimization”, in: G. Fandel and T. Gal (ed.), Multiple Criteria Decision Making, Theory and Application (Springer, Lecture Notes in Economics and Mathematical Systems No. 177, Berlin, 1980), p. 128–134.
  26. “Lösung nichtlinearer Optimierungsprobleme mit Nebenbedingungen”, in: H. Späth (ed.), Ausgewählte Operations Research Software in FORTRAN (Oldenbourg, München, 1979), p. 30–50.
  27. (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.
  28. “Zur Stabilität von Regressionskoeffizienten”, Operations Research Verfahren 33 (1979) 209–215.
  29. “Ein Algorithmus vom Typ der zulässigen Richtungen zur Lösung nichtlinearer Optimierungsprobleme mit Ungleichungsrestriktionen”, Operations Research Verfahren XXVIII (1978) 407–411.

Preprint

  1. (with F. Eibenstein and G. Leitmann) “On the Global Asymptotic Stabilization of Nonlinear Systems”, Preprint No. 838, Fachbereich Mathematik, TH Darmstadt (1984).

Online article

  1. “Nicht die Reichweite, sondern die Ladeinfrastruktur entscheidet”, SpringerProfessional, 12.12.2018 (link).

Patents

  1. (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.
  2. (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.