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A Semidefinite Programming approach for solving Multiobjective Linear Programming

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Abstract

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions of Multiobjective Linear Programmes (MOLPs). However, all of them are based on active-set methods (simplex-like approaches). We present a different method, based on a transformation of any MOLP into a unique lifted Semidefinite Program (SDP), the solutions of which encode the entire set of Pareto-optimal extreme point solutions of any MOLP. This SDP problem can be solved, among other algorithms, by interior point methods; thus unlike an active set-method, our method provides a new approach to find the set of Pareto-optimal solutions of MOLP.

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Authors and Affiliations

  1. Department of Quantitative Methods for Economics and Business, Universidad de Granada, Granada, Spain

    Victor Blanco

  2. IMUS, Universidad de Sevilla, Seville, Spain

    Justo Puerto & Safae El Haj Ben Ali

Authors
  1. Victor Blanco
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  2. Justo Puerto
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  3. Safae El Haj Ben Ali
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Corresponding author

Correspondence to Justo Puerto.

Additional information

The authors were partially supported by the projects Ref. FQM-5849 (Junta de Andalucía\(\backslash \)FEDER) and MTM2010-19576-C02-01 (MICINN, Spain). The first author was also supported by the research project Ref. FQM-343 (Junta de Andalucia).

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Blanco, V., Puerto, J. & El Haj Ben Ali, S. A Semidefinite Programming approach for solving Multiobjective Linear Programming. J Glob Optim 58, 465–480 (2014). https://doi.org/10.1007/s10898-013-0056-z

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