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A Semidefinite Programming approach for solving Multiobjective Linear Programming

A semidefinite programming approach for solving multiobjective linear programming
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 21 Mar 2013Embargo end date: 01 Jan 2011 Spain English Publisher:Springer Science and Business Media LLCJournal:Journal of Global Optimization, volume 58, pages 465-480 (issn: 0925-5001, eissn: 1573-2916, Copyright policy )
Authors: Víctor Blanco; Justo Puerto; Safae El-Haj Ben-Ali;

doi: 10.1007/s10898-013-0056-z , 10.48550/arxiv.1112.6075

arXiv: 1112.6075

handle: 11441/42760

A Semidefinite Programming approach for solving Multiobjective Linear Programming

Abstract

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.

13 pages, 1 figure

Country
Spain
Related Organizations
Keywords

Optimization and Control (math.OC), 90C29, 90C22, 90C05, 44A60, polynomial optimization, FOS: Mathematics, Semidefinite programming, moment problem, semidefinite programming, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), multiobjective linear programming, Mathematics - Optimization and Control, Multi-objective and goal programming

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    popularity
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    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Average
Average
Green
hybrid