Prof. Dr. Andreas Löhne

2024

• Andreas H. Hamel and Andreas Löhne. Multiple stage stochastic linear programming with multiple objectives: flexible decision making, preprintExterner Link (July 5, 2024).
• Andreas Löhne. The natural ordering cone of a polyhedral convex set-valued objective mapping. Optimization, online first (2024), articleExterner Link, preprintExterner Link.
• Daniel Dörfler and Andreas Löhne. Polyhedral approximation of spectrahedral shadows via homogenization. Journal of Optimization Theory and Applications  8 No.4 (2024), 549-569. articleExterner Link, preprintExterner Link.
• Daniel Dörfler and Andreas Löhne. Convex sets approximable as the sum of a compact set and a cone. Journal of Nonlinear and Variational Analysis  8 No.4 (2024), 681-689. articleExterner Link, preprintExterner Link
• Daniel Dörfler and Andreas Löhne. A polyhedral approximation algorithm for recession cones of spectrahedral shadows. Journal of Nonlinear and Variational Analysis, 2024. articleExterner Link, preprintExterner Link.

2023

• Andreas Löhne. A solution method for arbitrary polyhedral convex set optimization problems. preprintExterner Link (October 10, 2023), code of the numerical examplesExterner Link.
• Andreas Löhne. Existence of solutions for polyhedral convex set optimization problems. Optimization, online first (2024), articleExterner Link, preprintExterner Link.
• Andreas Löhne and Benjamin Weißing. Finite representation of quantile sets for multivariate data via vector linear programming. preprintExterner Link (March 27, 2023).
• Andreas Löhne. Approximate Vertex Enumeration. Journal of Computational Geometry  14 No.1 (2023), 257-286. articleExterner Link, preprintExterner Link, code of the numerical examplesExterner Link.
• Niklas Hey and Andreas Löhne. On unbounded polyhedral convex set optimization problems. To appear in: Minimax Theory and its Applications (accepted in 2023). preprintExterner Link.

2022

• Daniel Dörfler, Andreas Löhne, Christopher Schneider and Benjamin Weißing. A Benson-Type Algorithm for Bounded Convex Vector Optimization Problems with Vertex Selection. Optimization Software and Methods  37 No.3 (2022), 1006-1026. articleExterner Link, preprintExterner Link.

2021

• Andreas Löhne, Fangyuan Zhao and Lizhen Shao. On the approximation error for approximating convex bodies using multiobjective optimization. Applied Set-Valued Analysis and Optimization  3 (2021), 341-354. articleExterner Link, preprintExterner Link.

2020

• Simeon vom Dahl and Andreas Löhne. Solving polyhedral d.c. optimization problems via concave minimization. Journal of Global Optimization  78 No.1 (2020), 37-47. articleExterner Link, preprintExterner Link.

2019

• Daniel Ciripoi, Nidhi Kaihnsa, Andreas Löhne and Bernd Sturmfels. Computing Convex Hulls of Trajectories. Revista de la Unión Matemática Argentina  60 No.2 (2019), 637-662. articleExterner Link, preprintExterner Link.
• Andreas Löhne, Daniel Dörfler, Alexandra Rittmann, Benjamin Weißing. Solving bilevel problems with polyhedral constraint set. Journal of Applied and Numerical Optimization  1 No.3 (2019), 243-251. articleExterner Link.
• Daniel Ciripoi, Andreas Löhne and Benjamin Weißing. Calculus of convex polyhedra and polyhedral convex functions by utilizing a multiple objective linear programming solver. Published in: Optimization  68 No.10 (2019), 2039-2054. articleExterner Link, preprintExterner Link.
• Joachim Giesen, Sören Laue, Andreas Löhne and Christopher Schneider. Using Benson's Algorithm for Regularization Parameter Tracking. Proceedings of the 33d AAAI Conference on Artificial Intelligence (AAAI), (2019). articleExterner Link.

2018

• Daniel Dörfler and Andreas Löhne. Geometric duality and parametric duality for multiple objective linear programs are equivalent. Journal of Nonlinear and Convex Analysis  19 No.7 (2018), 1181-1188. articleExterner Link, preprintExterner Link.
• Andreas H. Hamel and Andreas Löhne. A set optimization approach to zero-sum matrix games with multi-dimensional payoffs. Mathematical Methods of Operations Research  88 No.3 (2018), 369–397. articleExterner Link, full-text view-only versionExterner Link, preprintExterner Link.
• Martin Bücker, Andreas Löhne, Benjamin Weißing and Gerhard Zumbusch. On parallelizing Benson's algorithm: limits and opportunities. Computational science and its applications—ICCSA 2018. Part II, 653–668, Lecture Notes in Comput. Sci., 10961, Springer, 2018. articleExterner Link.
• Daniel Ciripoi, Andreas Löhne and Benjamin Weißing. A vector linear programming approach for certain global optimization problems. Journal of Global Optimization  72 No.2 (2018), 347-372. articleExterner Link, preprintExterner Link.

2017

• Andreas Löhne and Andrea Wagner. Solving DC programs with polyhedral component utilizing a multiple objective linear programming solver. Journal of Global Optimization  69 No.2 (2017), 369-385. articleExterner Link, full-text view-only versionExterner Link, preprintExterner Link.
• Andreas Löhne and Benjamin Weißing. The vector linear program solver Bensolve -- notes on theoretical background. European Journal of Operational Research  260 No. 3 (2017), 807-813. articleExterner Link, preprintExterner Link.

2016

• Andreas Löhne and Benjamin Weißing. Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming. Mathematical Methods of Operations Research  84 No.2 (2016), 411-426. articleExterner Link, preprintExterner Link.

2015

• Andreas H. Hamel, Frank Heyde, Andreas Löhne, Birgit Rudloff and Carola Schrage. Set optimization - A rather short introduction. In: A. H. Hamel, F. Heyde, A. Löhne, B. Rudloff, and C. Schrage (eds.), Set Optimization and Applications in Finance - The State of the Art. From Set-Relations to Set-Valued Risk Measures. Springer Proceedings in Mathematics & Statistics, Vol. 151, Springer, 2015. articleExterner Link, preprintExterner Link.
• Andreas Löhne and Birgit Rudloff. On the dual of the solvency cone. Discrete Applied Mathematics 186 (2015), 176-185. articleExterner Link, preprintExterner Link.

2014

• Andreas Löhne. Projection of polyhedral cones and linear vector optimization. preprintExterner Link (June 06, 2014).
• Andreas Löhne, Birgit Rudloff, and Firdevs Ulus. Primal and Dual Approximation Algorithms for Convex Vector Optimization Problems. Journal of Global Optimization  60 No. 4 (2014), 713-736. article, Externer LinkpreprintExterner Link.
• Andreas Löhne and Birgit Rudloff. An algorithm for calculating the set of superhedging portfolios and strategies in markets with transaction costs. International Journal of Theoretical and Applied Finance 17 No. 2 (2014). articleExterner Link, preprintExterner Link.
• Andreas H. Hamel and Andreas Löhne. Lagrange duality in set optimization. Journal of Optimization Theory and Applications 161 No. 2 (2014), 368-397. article Externer Link, preprintExterner Link.
• Andreas H. Hamel, Andreas Löhne, and Birgit Rudloff. Benson type algorithms for linear vector optimization and applications. Journal of Global Optimization  59 No. 4 (2014), 811-836. articleExterner Link, preprintExterner Link.

2013

• Elvira Hernandez, Andreas Löhne, Luis Rodriguez-Marin and Christiane Tammer. Lagrange duality, stability and subdifferentials in vector optimization. Optimization  62 No. 3 (2013), 419-432. articleExterner Link, preprintExterner Link.
• Andreas Löhne and Carola Schrage. An Algorithm to Solve Polyhedral Convex Set Optimization Problems. Optimization  62 No. 1 (2013), 131-141. articleExterner Link, preprintExterner Link.

2012

• Matthias Ehrgott,  Andreas Löhne and Lizhen Shao. A dual variant of Benson's outer approximation algorithm. Journal of Global Optimization  52 No. 4 (2012), 757-778. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 12, 2007: download pdfExterner Link.

2011

• Andreas Löhne and Frank Heyde. Solution concepts in vector optimization. A fresh look at an old story. Optimization  60 No. 12 (2011), 1421-1440. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 19, 2008: download pdfExterner Link.

2010

• Radu Ian Bot and Andreas Löhne. On totally Fenchel unstable functions in finite dimensional spaces. Math. Programming  123 No. 1 (2010), 25-30. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 01, 2008: download pdfExterner Link.

2009

• Frank Heyde, Andreas Löhne, and Christiane Tammer. Set-valued duality theory for multiple objective linear programs and application to mathematical finance. Mathematical Methods of Operations Research  69 No. 1 (2009), 159-179. articleExterner Link, Martin Luther University Halle-Wittenberg, Preprint: Report of the Institute of Mathematics No. 04, 2007: download pdfExterner Link.

2008

• Andreas Löhne. A characterization of maximal monotone operators. Journal of Set-valued Analysis  16 No. 5/6 (2008), 663-700. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 06, 2007: download pdfExterner Link.
• Andreas Löhne. On semicontinuity of convex-valued multifunctions and Cesari's property (Q). Journal of Convex Analysis  15 No. 4 (2008), 803-818. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 04, 2005: download pdfExterner Link (former title: Semicontinuity of convex-valued multifunctions).
• Frank Heyde and Andreas Löhne. Geometric duality in multiple objective linear programming. SIAM Journal of Optimization  19 No. 2 (2008), 836-845. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 15, 2006: download pdfExterner Link.

2007

• Andreas Löhne and Christiane Tammer. A new approach to duality in vector optimization. Optimization  56 No. 1/2 (2007), 221-239. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 08,  2005: download pdfExterner Link.

2006

• Andreas Löhne and Constantin Zǎlinescu. On convergence of closed convex sets. Journal of Mathematical Analysis and Applications  319 No. 2 (2006), 617-634. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 02, 2005: download pdfExterner Link.
• Andreas Löhne. On convex functions with values in conlinear spaces. Journal of Nonlinear and Convex Analysis  7 No. 1 (2006), 115-122. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 07, 2003: download pdfExterner Link.
• Andreas Hamel and Andreas Löhne. Minimal element theorems and Ekeland's principle with set relations. Journal of Nonlinear and Convex Analysis  7 No. 1 (2006), 19-37. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 11, 2002: download pdfExterner Link (former title: Minimal set theorems).

2005

• Andreas Löhne. Optimization with set relations: Conjugate duality. Optimization  54 No. 3 (2005), 265-282. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 17, 2004: download pdfExterner Link.

2004

• Andreas Hamel, Frank Heyde, Andreas Löhne, Christiane Tammer and Kristin Winkler. Closing the duality gap in linear vector optimization. Journal of Convex Analysis  11 No. 1 (2004), 163-178. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 08, 2004: download pdfExterner Link.

2003

• Andreas Hamel and Andreas Löhne. Minimal point theorems in uniform spaces. In: Agarval R. P., O'Regan, D. (eds.), Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, Kluwer Academic Publishers, Dordrecht, 2003. articleExterner Link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 09, 2002: download pdfExterner Link.

• Andreas Löhne. Vector Optimization with Infimum and Supremum. Springer, 2011, 1st Edition., 206 p. 26 illus. Hardcover, ISBN 978-3-642-18350-8, bookExterner Link
• Andreas Löhne. Duality in Vector Optimization with Infimum and Supremum. Chapter 3 in:  Ansari, Q.H.; Yao, J.-C. (Eds.): Recent Developments in Vector Optimization. Springer, 2011Externer Link, 1st Edition., 2011, XXIV, 547 p.

https://arxiv.org/a/lohne_a_1.htmlExterner Link

Habilitation thesis: Vector Optimization with Infimum and Supremum (an extended version is published by Springer, see above)

Ph.D. thesis: Optimization with set relationsExterner Link

Master's thesis: Minimal point theorems in uniform spaces and related assertions (in German)Externer Link

• Frank Heyde, Andreas Löhne and Christiane Tammer. The attainment of the solution of the dual program in vertices for vectorial linear programs. In: Barichard, Vincent (ed.) et al., Multiobjective programming and goal programming. Theoretical results and practical applications. Selected papers based on the presentations at the international conference on multiobjective programming and goal programming (MOP/GP 2006), Tours, France, June 12-14, 2006. Berlin: Springer. Lecture Notes in Economics and Mathematical Systems 618, 13-24 (2009), Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 16, 2006: download pdfExterner Link
• Andreas Löhne. On conjugate duality in optimization with set relations. In: Geldermann, J.; Treitz, M. (eds.):
  Entscheidungstheorie und -praxis in industrieller Produktion und Umweltforschung,
  Shaker, Aachen, 2004, overview of: Optimization with set relations: Conjugate duality
• Wolfgang W. Breckner, Andreas H. Hamel, Andreas Löhne and  Christiane Tammer. Necessary and sufficient conditions for approximate saddle points. In: Geldermann, J.; Treitz, M. (eds.): Entscheidungstheorie und -praxis in industrieller Produktion und Umweltforschung, Shaker, Aachen, 2004  

seit 11/2015 - Professor an der Friedrich-Schiller-Universität Jena

07/2015 - Angebot auf eine W3-Professur an der Universität Mannheim, abgelehnt

06/2015 - Angebot auf eine W2-Professur an der Friedrich-Schiller-Universität Jena, angenommen

04/2005 - 09/2015 - Wissenschaftlicher Mitarbeiter an der MLU Halle-Wittenberg

03/2005 - 03/2005 - Stipendium des DAAD (Deutscher Akademischer Austauschdienst)

01/2005 - 02/2005 - Stipendium der „Gesellschaft der Freunde und Förderer der MLU“

02/2002 - 12/2004 - Graduiertenstipendium des Landes Sachsen-Anhalt

12/2001 - 01/2002 - Lehrauftrag an der MLU Halle-Wittenberg

10/1997 - 11/2001 - Student an der MLU Halle-Wittenberg (Mathematik, bis 09/1999 auch Physik)

09/1994 - 08/1997 - Gymnasium (Zweiter Bildungsweg)

09/1989 - 08/1994 - Berufsausbildung und Berufstatigkeit (Elektroinstallateur)

03/2013 (1 Monat) - Princeton University (USA / New Jersey)

03/2012 (1 Monat) - Princeton University (USA / New Jersey)

02/2011 (5 Monate) - Visiting Assistant Professor an der Princeton University (USA / New Jersey)

02/2008 (1 Monat) - Universitat Autonoma Barcelona (Spanien)

04/2006 (1 Monat) - Department of Engineering, The University of Auckland (Neuseeland)

03/2005 (1 Monat) - University ''Babes Bolyai'' Cluj-Napoca (Rumänien) und University ''A. I. Cuza'' Iasi (Rumänien)

03/2003 (2 Monate) -- Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig (Deutschland)

10/2010 - Habilitation

05/2005 - Promotion (Dr. rer nat.)

11/2001 - Diplom in Mathematik

09/1999 - Vordiplom in Mathematik

09/1999 - Vordiplom in Physik