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

Evgeny Shindin, Gideon Weiss

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)157-201
Number of pages45
JournalMathematical Programming
Issue number1-2
StatePublished - 1 Mar 2020

Bibliographical note

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.


  • Continuous linear programming
  • Optimal control
  • Simplex-type algorithm

ASJC Scopus subject areas

  • Software
  • General Mathematics


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