Andreas Löhne

Professor of Mathematical Optimization

Publications

  • Peer-reviewed publications

    Preprints / Submitted Articles

    2024

    2023

    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. articleExternal link, preprintExternal 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. articleExternal link, preprintExternal 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. articleExternal link, preprintExternal 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. articleExternal link, preprintExternal 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. articleExternal 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. articleExternal link, preprintExternal link.
    • Joachim Giesen, Sören Laue, Andreas Löhne and Christopher Schneider. Using Benson's Algorithm for Regularisation Parameter Tracking. Proceedings of the 33d AAAI Conference on Artificial Intelligence (AAAI), (2019). articleExternal 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. articleExternal link, preprintExternal 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. articleExternal link, full-text view-only versionExternal link, preprintExternal link.
    • Martin Bücker, Andreas Löhne, Benjamin Weißing and Gerhard Zumbusch. On parallelising 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. articleExternal 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. articleExternal link, preprintExternal link.

    2017

    2016

    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. articleExternal link, preprintExternal link.
    • Andreas Löhne and Birgit Rudloff. On the dual of the solvency cone. Discrete Applied Mathematics 186 (2015), 176-185. articleExternal link, preprintExternal link.

    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, External linkpreprintExternal 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). articleExternal link, preprintExternal 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 External link, preprintExternal 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. articleExternal link, preprintExternal 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. articleExternal link, preprintExternal link.
    • Andreas Löhne and Carola Schrage. An Algorithm to Solve Polyhedral Convex Set Optimization Problems. Optimization 62 No. 1 (2013), 131-141. articleExternal link, preprintExternal 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. articleExternal link, preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 12, 2007: download pdfExternal 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. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 19, 2008: download pdfExternal 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. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 01, 2008: download pdfExternal 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. articleExternal link, Martin Luther University Halle-Wittenberg, Preprint: Report of the Institute of Mathematics No. 04, 2007: download pdfExternal link.

    2008

    • Andreas Löhne. A characterisation of maximal monotone operators. Journal of Set-valued Analysis 16 No. 5/6 (2008), 663-700. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 06, 2007: download pdfExternal link.
    • Andreas Löhne. On semicontinuity of convex-valued multifunctions and Cesari's property (Q). Journal of Convex Analysis 15 No. 4 (2008), 803-818. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 04, 2005: download pdfExternal 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. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Mathematics No. 15, 2006: download pdfExternal link.

    2007

    • Andreas Löhne and Christiane Tammer. A new approach to duality in vector optimization. Optimization 56 No. 1/2 (2007), 221-239. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 08, 2005: download pdfExternal 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. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 02, 2005: download pdfExternal link.
    • Andreas Löhne. On convex functions with values in conlinear spaces. Journal of Nonlinear and Convex Analysis 7 No. 1 (2006), 115-122. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 07, 2003: download pdfExternal 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. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 11, 2002: download pdfExternal link (former title: Minimal set theorems).

    2005

    • Andreas Löhne. Optimization with set relations: Conjugate duality. Optimization 54 No. 3 (2005), 265-282. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 17, 2004: download pdfExternal 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. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 08, 2004: download pdfExternal 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. articleExternal link, Preprint: Martin Luther University Halle-Wittenberg, Report of the Institute of Optimization and Stochastics No. 09, 2002: download pdfExternal link.
    Learn moreExternal link
  • Book and book chapters
  • ArXiv preprints
  • Theses

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

    PhD thesis: Optimization with set relationsExternal link

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

  • Other publications
    • 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 pdfExternal 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

Mathematical Software

  • Bensolve

    BENSOLVE is a solver for vector linear programs (VLP), in particular, for the subclass of multiple objective linear programs (MOLP). It is based on Benson's algorithm and its extensions. BENSOLVE is a free software published under the terms of the GNU General Public License. It utilizes the GNU Linear Programming Kit (GLPK). BENSOLVE (from version 2) is written in C programming language.

    For further information and to download the latest version, visit:  

    www.bensolve.orgExternal link

    or use the following link to a local repositoryExternal link. 

  • Bensolve Tools

    BENSOLVE TOOLS is an Octave/Matlab toolbox for polyhedral calculus and and polyhedral optimization. It is based on the VLP solver BENSOLVE. The main features of the current version are:

    • Calculus of convex polyhedra
      • computing H-representation and V-representation
      • computing an inequality representation (H-representation)
      • image and inverse image under linear transformation
      • lineality space, affine hull, dimension, recession cone
      • conic hull of a polyhedron
      • adjacency list, facet-vertex incidence list
      • Minkowski sum of n polyhedra
      • intersection and closed convex hull of the union of n polyhedra
      • cartesian product of n polyhedra
      • polar and polar cone of a polyhedron
      • normal cone of a polyhedron at a point
      • comparing polyhedra: subset, proper subset, equality
      • plotting 2d and 3d polyhedra
    • Calculus of polyhedral convex functions
      • pointwise maximum of n polyhedral functions
      • lower closed convex envelope of n polyhedral functions
      • infimal convolution of n polyhedral functions
      • pointwise sum of n polyhedral functions
      • conjugate of a polyhedral function
      • recession function of a polyhedral function
      • domain, range, level sets, recession cone of a polyhedral function
      • subdifferential at some point
      • test for pointwise ordering and equality of two polyhedral functions
      • plot of polyhedral functions with one or two variables
    • Solving Linear Programs and Polyhedral Convex Programs (GLPK interface)
    • Global Optimization
      • quasi-convace objective and linear constraints
      • possibility to exploit cone monotonicity
    • Multiobjective linear programming (MOLP)
    • Vector linear programming (VLP)

    For further information and to download the latest version, visit:

    http://tools.bensolve.orgExternal link

    or use the following link to a local repositoryExternal link. 

Academic career

  • Positions and scholarships

    since 11/2015 - Professor at the Friedrich Schiller University Jena

    07/2015 - Offer for a professorship paid on salary scale W3 at the University of Mannheim, rejected

    06/2015 - Offer for a professorship paid on salary scale W2 at the Friedrich Schiller University Jena, accepted

    04/2005 - 09/2015 - Research assistant at the MLU Halle-Wittenberg

    03/2005 - 03/2005 - Scholarship of the DAAD (German Academic Exchange Service)

    01/2005 - 02/2005 - Scholarship of the "Society of Friends and Sponsors of MLU"

    02/2002 - 12/2004 - Graduate scholarship of the state of Saxony-Anhalt

    12/2001 - 01/2002 - Teaching contract at the MLU Halle-Wittenberg

    10/1997 - 11/2001 - Student at MLU Halle-Wittenberg (Mathematics, until 09/1999 also Physics)

    09/1994 - 08/1997 - grammar school (second route into education)

    09/1989 - 08/1994 - Vocational training and employment (electrician)

  • Guest stays

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

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

    02/2011 (5 months) - Visiting Assistant Professor at Princeton University (USA / New Jersey)

    02/2008 (1 month) - Universitat Autonoma Barcelona (Spain)

    04/2006 (1 month) - Department of Engineering, The University of Auckland (New Zealand)

    03/2005 (1 month) - University ''Babes Bolyai'' Cluj-Napoca (Romania) and University ''A. I. Cuza'' Iasi (Romania)

    03/2003 (2 months) - Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany)

  • Degrees

    10/2010 - Habilitation

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

    11/2001 - Diploma in Mathematics

    09/1999 - Pre-diploma in Mathematics

    09/1999 - Pre-diploma in Physics

Contact details

Andreas Löhne, Univ.-Prof. Dr
vCard
Room 3305
Ernst-Abbe-Platz 2
07743 Jena Google Maps site planExternal link