A Semidefinite Programming approach for solving Multiobjective Linear Programming |
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Authors: | Victor Blanco Justo Puerto Safae El Haj Ben Ali |
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Institution: | 1. Department of Quantitative Methods for Economics and Business, Universidad de Granada, Granada, Spain 2. IMUS, Universidad de Sevilla, Seville, Spain
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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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