Automation and Remote Control

, Volume 77, Issue 9, pp 1633–1648 | Cite as

A new effective dynamic program for an investment optimization problem

  • E. R. GafarovEmail author
  • A. Dolgui
  • A. A. Lazarev
  • F. Werner
Control in Social Economic Systems, Medicine, and Biology


After a series of publications of T.E. O’Neil et al. (e.g. in 2010), dynamic programming seems to be the most promising way to solve knapsack problems. Some techniques are known to make dynamic programming algorithms (DPA) faster. One of them is the graphical method that deals with piecewise linear Bellman functions. For some problems, it was previously shown that the graphical algorithm has a smaller running time in comparison with the classical DPA and also some other advantages. In this paper, an exact graphical algorithm (GrA) and a fully polynomial-time approximation scheme based on it are presented for an investment optimization problem having the best known running time. The algorithms are based on new Bellman functional equations and a new way of implementing the GrA.


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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • E. R. Gafarov
    • 1
    Email author
  • A. Dolgui
    • 2
  • A. A. Lazarev
    • 3
    • 4
    • 5
  • F. Werner
    • 6
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  2. 2.Ecole Nationale Supérieure des MinesIRCCYN, UMR CNRS 6597NantesFrance
  3. 3.Lomonosov Moscow State UniversityMoscowRussia
  4. 4.Moscow Institute of Physiscs and TechnologyDolgoprudnyRussia
  5. 5.International Laboratory of Decision Choice and Analysis, National Research UniversityHigher School of EconomicsMoscowRussia
  6. 6.Fakultät für MathematikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

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