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

  • Evgeny Shindin
  • Gideon Weiss
Full Length Paper Series A

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. Specifically, 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 formulated a symmetric dual and have shown strong duality. 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.

Keywords

Optimal control Continuous linear programming Simplex-type algorithm 

Mathematics Subject Classification

90C05 49N05 65K05 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  1. 1.IBM ResearchHaifaIsrael
  2. 2.Department of StatisticsThe University of HaifaHaifaIsrael

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