Dr. Axel Dreves

Professur für Ingenieur-Mathematik (Prof. Gerdts)
Gebäude 41/300, Zimmer 2304
+49 89 6004-2129
axel.dreves@unibw.de

Dr. Axel Dreves

Preprints

  • Dreves, A., Gerdts, M., Sama, M., D'Ariano, A.: Free flight trajectory optimization and generalized Nash equilibria in conflicting situations (Januar 2017)

Journal Artikel

  1. Dreves, A.: Linear and superlinear convergence of a potential reduction algorithm for generalized Nash equilibrium problems. Minimax Theory and its Applications 9 (1), 55--84 (2024)
  2. De Marchi, A., Dreves, A., Gerdts, M., Gottschalk, S., Rogovs, S.: A Function Approximation Approach for Parametric
    Optimization,  J. Optim. Theory Appl. 196, 56--77 (2023), DOI 10.1007/s10957-022-02138-4, Open-Acess PDF
  3. Britzelemeier, A., Dreves, A.: A Decomposition Algorithm for Nash Equilibria in Intersection Management. Optimization 70 (11), 2441--2478, (2021), DOI 10.1080/02331934.2020.1786088 PDF
  4. Dreves, A., Sagratella, S.: Nonsingularity and stationarity results for quasi-variational inequalities. J. Optim. Theory Appl. 185(3), 711--743, (2020), DOI 10.1007/s10957-020-01678-x, Open Access PDF
  5. Dreves, A.: A best-response approach for equilibrium selection in 2-player generalized Nash equilibrium problems. Optimization 68(12), 2265--2291 (2019), DOI 10.1080/02331934.2019.1646743 PDF
  6. Britzelmeier, A., Dreves, A., Gerdts, M.: Numerical solution of potential games arising in the control of cooperative automatic vehicles. 2019 Proceedings of the Conference on Control and its Applications, 38--45, DOI 10.1137/1.9781611975758.7
  7. Dreves, A.: An algorithm for equilibrium selection in generalized Nash equilibrium problems. Comput. Optim. Appl. 73, 821--837 (2019), DOI 10.1007/s10589-019-00086-w PDF
  8. Dreves, A.: How to select a solution in generalized Nash equilibrium problems. J. Optim. Theory Appl. 178(3), 973--997 (2018), DOI 10.1007/s10957-018-1327-0 PDF
  9. Dreves, A., Gerdts, M.: A generalized Nash equilibrium approach for optimal control problems of autonomous cars. Optimal Control Appl Methods 39, 326-- 342 (2018), DOI 10.1002/oca.2348
  10. Dreves, A., Gwinner, J., Ovcharova, N.: On the Use of Elliptic Regularity Theory for the Numerical Solution of Variational Problems. In N.J. Daras, T.M. Rassias: Operations Research, Engineering, and Cyber Security: Trends in Applied Mathematics and Technology, 231--257 (2017), DOI 10.1007/978-3-319-51500-7_11
  11. Dreves, A.: Computing all solutions of linear generalized Nash equilibrium problems.

    Math. Methods Oper. Res. 85(2), 207--221 (2017), DOI 10.1007/s00186-016-0562-0 PDF

  12. Dreves, A.: A Nash equilibrium approach for multiobjective optimal control problems with elliptic partial differential equations. Control Cybernet. 45(4), 457--482 (2016)
  13. Dreves, A., Sudermann-Merx, N.: Solving linear generalized Nash equilibrium problems numerically.

    Optim. Methods Softw. 31:5,1036--1063 (2016) DOI 10.1080/10556788.2016.1165676

  14. Dreves, A., Gwinner, J.: Jointly convex generalized Nash equilibria and elliptic multiobjective optimal control. J. Optim. Theory Appl. 168, 1065--1086 (2016), DOI 10.1007/s10957-015-0788-7
  15. Dreves, A.: Uniqueness for quasi-variational inequalities.

    Set-Valued Var. Anal. 24, 285--297 (2016), DOI 10.1007/s11228-015-0339-2 PDF

  16. Dreves, A.: Improved error bound and a hybrid method for generalized Nash equilibrium problems.

    Comput. Optim. Appl. 65 (2), 431--448 (2016), DOI 10.1007/s10589-014-9699-z PDF

  17. Dreves, A.: Finding all solutions of affine generalized Nash equilibrium problems with one-dimensional strategy sets. Math. Methods Oper. Res. 80, 139--159 (2014), DOI 10.1007/s00186-014-0473-x
  18. Dreves, A., Facchinei, F., Fischer, A., Herrich, M.: A new error bound result for Generalized Nash Equilibrium Problems and its algorithmic application. Comput. Optim. Appl. 59, 63--84 (2014), DOI 10.1007/s10589-013-9586-z

  19. Dreves, A., von Heusinger, A., Kanzow, C., Fukushima, M.: A globalized Newton method for the computation of normalized Nash equilibria. J. Global Optim. 56, 327--340 (2013), DOI 10.1007/s10898-011-9824-9

  20. Dreves, A., Kanzow, C., Stein, O.: Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems. J. Global Optim. 53, 587--614 (2012), DOI 10.1007/s10898-011-9727-9

  21. Dreves, A., Facchinei, F., Kanzow, C., Sagratella, S.: On the solution of the KKT conditions of generalized Nash equilibrium problems. SIAM J. Optim. 21, 1082--1108 (2011), DOI 10.1137/100817000

  22. Dreves, A., Kanzow, C.: Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems. Comput. Optim. Appl. 50, 23--48 (2011), DOI 10.1007/s10589-009-9314-x

Dissertation

  • Globally Convergent Algorithms for the Solution of Generalized Nash Equilibrium Problems.

    Dissertation, University of Würzburg (2012),

    http://opus.bibliothek.uni-wuerzburg.de/volltexte/2012/6982

 

Lehrveranstaltungen:

Vorlesungen

Optimierung Bachelor ME, 4 WT 23
Optimierung Master ME, 2 FT 20
Lineare und nichtlineare Optimierung Bachelor LRT, 3 FT 24
Lineare und nichtlineare Optimierung Bachelor LRT, 7 HT 15
Einführung in die Numerik Bachelor ME, 5 WT 15

Übungen

Mathematik I Bachelor LRT, 1 HT24, HT23, HT22, HT21, HT20, HT 19, HT 18, HT 17, HT 16
Mathematik II Bachelor LRT, 1 HT24, HT23, HT22, HT21, HT20, HT 19, HT 18, HT 17, HT16, HT14
Matthematik III Bachelor LRT, 2 WT 24, WT 20, WT 19, WT 18, WT 14
Optimierung Bachelor ME, 4 WT23
Optimierung Master ME, 2 FT 20, FT 19, FT 18, FT 17, FT 16, WT 13
Lineare und nichtlineare Optimierung Bachelor LRT, 7, 3 FT24, HT 15
Mathematische Methoden in den Ingenieurwissenschaften Master LRT, 1 WT22, WT21, WT 17, WT 16
Numerische Mathematik I Bachelor LRT, 3 FT 13
Einführung in die Numerik Bachelor ME, 5 WT 15
Partielle Differentialgleichungen I Master ME, 3 HT 13
Partielle Differentialgleichungen II Master ME, 4 WT 14
Funktionalanalysis Master ME, 3 HT 12