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Generalized Goal Programming: polynomial methods and applications

Generalized Goal Programming: polynomial methods and applications
Generalized Goal Programming: polynomial methods and applications
In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework.
In spite of its generality, this problem can be analyzed from a geometrical and a computational viewpoint, and a unified solution methodology can be given. Indeed, a dual is derived, enabling us to describe the set of optimal solutions geometrically. Moreover, Interior-Point methods are described which yield an e-optimal solution in polynomial time.
goal programming, closest points, interior point methods, location, regression
0025-5610
281-303
Carrizosa, Emilio
dc7a6a8a-fc2f-457f-9e79-978cab4fe435
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Carrizosa, Emilio
dc7a6a8a-fc2f-457f-9e79-978cab4fe435
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98

Carrizosa, Emilio and Fliege, Jörg (2002) Generalized Goal Programming: polynomial methods and applications. Mathematical Programming, 93 (2), 281-303. (doi:10.1007/s10107-002-0303-4).

Record type: Article

Abstract

In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework.
In spite of its generality, this problem can be analyzed from a geometrical and a computational viewpoint, and a unified solution methodology can be given. Indeed, a dual is derived, enabling us to describe the set of optimal solutions geometrically. Moreover, Interior-Point methods are described which yield an e-optimal solution in polynomial time.

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More information

Submitted date: December 2002
Published date: December 2002
Keywords: goal programming, closest points, interior point methods, location, regression
Organisations: Operational Research

Identifiers

Local EPrints ID: 48821
URI: http://eprints.soton.ac.uk/id/eprint/48821
ISSN: 0025-5610
PURE UUID: 9a7a0980-fade-4f5b-b262-360c73582029
ORCID for Jörg Fliege: ORCID iD orcid.org/0000-0002-4459-5419

Catalogue record

Date deposited: 15 Oct 2007
Last modified: 18 Feb 2021 17:10

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Contributors

Author: Emilio Carrizosa
Author: Jörg Fliege ORCID iD

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