A semidefinite programming approach for solving Multiobjective Linear Programming

Details A semidefinite programming approach for solving Multiobjective Linear Programming A semidefinite programming approach for solving Multiobjective Linear Programming

2011-12-28

arxiv.org/abs/1112.6075v1

Mathematics

Optimization and Control

13 pages, 1 figure

Scientific paper

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.

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