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Primal and dual approximation algorithms for convex vector optimization problems
Löhne, Andreas; Rudloff, Birgit; Ulus, Firdevs - In: Journal of Global Optimization 60 (2014) 4, pp. 713-736
Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson’s outer approximation algorithm, and the second one is a dual variant...
Persistent link: https://www.econbiz.de/10011151248
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Set-valued duality theory for multiple objective linear programs and application to mathematical finance
Heyde, Frank; Löhne, Andreas; Tammer, Christiane - In: Computational Statistics 69 (2009) 1, pp. 159-179
We develop a duality theory for weakly minimal points of multiple objective linear programs which has several … are hyperplanes. As in other set-valued (but not in vector-valued) approaches, there is no duality gap in the case that … in a complete lattice. Thus the duality theory has a high degree of analogy to its classical counterpart. Another …
Persistent link: https://www.econbiz.de/10010759327
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A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming
Ehrgott, Matthias; Löhne, Andreas; Shao, Lizhen - In: Journal of Global Optimization 52 (2012) 4, pp. 757-778
Persistent link: https://www.econbiz.de/10010994025
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Benson type algorithms for linear vector optimization and applications
Hamel, Andreas; Löhne, Andreas; Rudloff, Birgit - In: Journal of Global Optimization 59 (2014) 4, pp. 811-836
New versions and extensions of Benson’s outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous...
Persistent link: https://www.econbiz.de/10010994156
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Set-valued duality theory for multiple objective linear programs and application to mathematical finance
Heyde, Frank; Löhne, Andreas; Tammer, Christiane - In: Mathematical Methods of Operations Research 69 (2009) 1, pp. 159-179
We develop a duality theory for weakly minimal points of multiple objective linear programs which has several … are hyperplanes. As in other set-valued (but not in vector-valued) approaches, there is no duality gap in the case that … in a complete lattice. Thus the duality theory has a high degree of analogy to its classical counterpart. Another …
Persistent link: https://www.econbiz.de/10010999730