242
Views
6
CrossRef citations to date
0
Altmetric
Articles

Calculus of convex polyhedra and polyhedral convex functions by utilizing a multiple objective linear programming solver

, &
Pages 2039-2054 | Received 31 Jan 2018, Accepted 26 Aug 2018, Published online: 21 Sep 2018

References

  • Löhne A, Weißing B. Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming. Math Methods Operat Res. 2016;84(2):411–426. doi: 10.1007/s00186-016-0554-0
  • Rockafellar R. Convex analysis. Princeton (NJ): Princeton University Press; 1972.
  • Lauritzen N. Undergraduate convexity. From Fourier and Motzkin to Kuhn and Tucker. Hackensack (NJ): World Scientific; 2013.
  • Weißing B. The polyhedral projection problem [PhD thesis]. Jena: Friedrich Schiller University Jena; 2017.
  • Lovàsz L, Schrijver A. Matrix cones, projection representations, and stable set polyhedra. Proceedings of DIMACS Workshop on Polyhedral Combinatorics 1990; 1989:1–17.
  • Herceg M, Kvasnica M, Jones C, Morari M. Multi-parametric toolbox 3.0. Proceedings of the European Control Conference, Zürich, Switzerland; 2013 July 17–19. p. 502–510. [cited 2018 January 4]. Available from: http://control.ee.ethz.ch/mpt.
  • Güler O. Foundations of optimization. New York (NY): Springer; 2010.
  • Benson HP. An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem. J Global Optim. 1998;13(1):1–24. doi: 10.1023/A:1008215702611
  • Hamel AH, Löhne A, Rudloff B. Benson type algorithms for linear vector optimization and applications. J Global Optim. 2014;59(4):811–836. doi: 10.1007/s10898-013-0098-2
  • Löhne A. Vector optimization with infimum and supremum. Vector Optimization. Heidelberg: Springer; 2011.
  • Heyde F, Löhne A. Geometric duality in multiple objective linear programming. SIAM J Optim. 2008;19(2):836–845. doi: 10.1137/060674831
  • Ciripoi D, Löhne A, Weißing B. Bensolve tools – calculus of convex polyhedra, calculus of polyhedral convex functions, global optimization, vector linear programming for Octave and Matlab, Version 1.1. Available from: http://tools.bensolve.org.
  • Löhne A, Weißing B. Bensolve - a free vector linear program solver, version 2.1. Available from: http://bensolve.org.
  • Ciripoi D, Löhne A, Weißing B. A vector linear programming approach for certain global optimization problems. J Global Optim. 2017. Available from: http://arxiv.org/abs/1705.02297.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.