Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming

Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective linear programming. The number of objectives of the multipl...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Vol. 84; no. 2; pp. 411 - 426
Main Authors: Lohne, Andreas, Weising, Benjamin
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2016
Springer Nature B.V
Subjects:
Business and Management
Calculus of Variations and Optimal Control; Optimization
Equivalence
Inequalities
Linear programming
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiple objective
Operations research
Operations Research/Decision Theory
Optimization
Order disorder
Original Article
Polyhedra
Projection
Studies
Vectors (mathematics)
Irredundant solution
Representation of polyhedra
52B55
15A39
Vector linear programming
90C29
Linear vector optimization
Multi-objective optimization
90C05
ISSN:1432-2994, 1432-5217
Online Access:Get full text
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Summary:Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective linear programming. The number of objectives of the multiple objective linear program is by one higher than the dimension of the projected polyhedron. The result implies that an arbitrary vector linear program (with arbitrary polyhedral ordering cone) can be solved by solving a multiple objective linear program (i.e. a vector linear program with the standard ordering cone) with one additional objective space dimension.
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ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-016-0554-0