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Primal and Dual Approximation Algorithms for Convex Vector Optimization Problems

Author(s): Löhne, Andreas; Rudloff, Birgit; Ulus, Firdevs

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Abstract: 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 of it. Both algorithms provide an inner as well as an outer approximation of the (upper and lower) images. Only one scalar convex program has to be solved in each iteration. We allow objective and constraint functions that are not necessarily differentiable, allow solid pointed polyhedral ordering cones, and relate the approximations to an appropriate e-solution concept. Numerical examples are provided.
Publication Date: Dec-2014
Electronic Publication Date: 12-Jan-2014
Citation: Löhne, Andreas, Rudloff, Birgit, Ulus, Firdevs. (2014). Primal and Dual Approximation Algorithms for Convex Vector Optimization Problems. Journal of Global Optimization, 60 (4), 713 - 736. doi:10.1007/s10898-013-0136-0
DOI: doi:10.1007/s10898-013-0136-0
ISSN: 0925-5001
EISSN: 1573-2916
Pages: 713 - 736
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Global Optimization
Version: Author's manuscript

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