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A geometric algorithm for multi-parametric linear programming

Borrelli, Francesco and Bemporad, Alberto and Morari, Manfred A geometric algorithm for multi-parametric linear programming. Journal of Optimization Theory and Applications, 118 (3). pp. 515-540. ISSN 0022-3239 (2003)

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We propose a novel algorithm for solving multiparametric linear programming problems. Rather than visiting different bases of the associated LP tableau, we follow a geometric approach based on the direct exploration of the parameter space. The resulting algorithm has computational advantages, namely the simplicity of its implementation in a recursive form and an efficient handling of primal and dual degeneracy. Illustrative examples describe the approach throughout the paper. The algorithm is used to solve finite-time constrained optimal control problems for discrete-time linear dynamical systems.

Item Type: Article
Identification Number: 10.1023/B:JOTA.0000004869.66331.5c
Uncontrolled Keywords: Multiparametric programming; sensitivity analysis; postoptimality analysis; linear programming; optimal control
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Professor Alberto Bemporad
Date Deposited: 27 Jul 2011 09:04
Last Modified: 05 Aug 2011 14:04
URI: http://eprints.imtlucca.it/id/eprint/450

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