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A semidefinite programming approach for solving Multiobjective Linear Programming

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all Pareto-optimal solutions of MOLP. We present an explicit construction, based on a transformation of any MOLP into a finite sequence of SemiDefinite Programs (SDP), the solutions of which give the entire set of Pareto-optimal extreme points solutions of MOLP. These SDP problems are solved by interior point methods; thus our approach provides a pseudo-polynomial interior point methodology to find the set of Pareto-optimal solutions of MOLP.

preprint2011arXivOpen access
Víctor BlancoJusto PuertoSafae El-Haj Ben-Ali
math.ACmath.OC
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Víctor BlancoJusto PuertoSafae El-Haj Ben-Ali

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