A simplex-type algorithm for continuous linear programs with constant coefficients

We consider continuous linear programs over a continuous finite time horizon \(T\), with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space of measures or of functions of bounded variation. These m...

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Podrobná bibliografie
Vydáno v:	arXiv.org
Hlavní autoři:	Shindin, Evgeny, Weiss, Gideon
Médium:	Paper
Jazyk:	angličtina
Vydáno:	Ithaca Cornell University Library, arXiv.org 01.05.2019
Témata:	Algorithms Coefficients Combinatorial analysis Linear programming Mathematical models Matrix methods Simplex method
ISSN:	2331-8422
On-line přístup:	Získat plný text
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Popis
Shrnutí:	We consider continuous linear programs over a continuous finite time horizon \(T\), with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the separated continuous linear programming models and their various duals, as formulated in the past by Anderson, by Pullan, and by Weiss. In previous papers we have shown that these problems possess optimal strongly dual solutions. We also have presented a detailed description of optimal solutions and have defined a combinatorial analogue to basic solutions of standard LP. In this paper we present an algorithm which solves this class of problems in a finite bounded number of steps, using an analogue of the simplex method, in the space of measures.
Bibliografie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1705.04959