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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Published in:arXiv.org
Main Authors: Shindin, Evgeny, Weiss, Gideon
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 01.05.2019
Subjects:
Algorithms
Coefficients
Combinatorial analysis
Linear programming
Mathematical models
Matrix methods
Simplex method
ISSN:2331-8422
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Abstract 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.
AbstractList 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.
Author Shindin, Evgeny
Weiss, Gideon
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SubjectTerms Algorithms
Coefficients
Combinatorial analysis
Linear programming
Mathematical models
Matrix methods
Simplex method
Title A simplex-type algorithm for continuous linear programs with constant coefficients
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