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Solving infinite horizon optimization problems through analysis of a one-dimensional global optimization problem

Author

Listed:
  • Seksan Kiatsupaibul

    (Chulalongkorn University)

  • Robert L. Smith

    (The University of Michigan)

  • Zelda B. Zabinsky

    (University of Washington)

Abstract

Infinite horizon optimization (IHO) problems present a number of challenges for their solution, most notably, the inclusion of an infinite data set. This hurdle is often circumvented by approximating its solution by solving increasingly longer finite horizon truncations of the original infinite horizon problem. In this paper, we adopt a novel transformation that reduces the infinite dimensional IHO problem into an equivalent one dimensional optimization problem, i.e., minimizing a Hölder continuous objective function with known parameters over a closed and bounded interval of the real line. We exploit the characteristics of the transformed problem in one dimension and introduce an algorithm with a graphical implementation for solving the underlying infinite dimensional optimization problem.

Suggested Citation

  • Seksan Kiatsupaibul & Robert L. Smith & Zelda B. Zabinsky, 2016. "Solving infinite horizon optimization problems through analysis of a one-dimensional global optimization problem," Journal of Global Optimization, Springer, vol. 66(4), pages 711-727, December.
    • Handle: RePEc:spr:jglopt:v:66:y:2016:i:4:d:10.1007_s10898-016-0423-7
    DOI: 10.1007/s10898-016-0423-7
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    References listed on IDEAS

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    1. Jeffrey M. Alden & Robert L. Smith, 1992. "Rolling Horizon Procedures in Nonhomogeneous Markov Decision Processes," Operations Research, INFORMS, vol. 40(3-supplem), pages 183-194, June.
    2. James C. Bean & Robert L. Smith, 1984. "Conditions for the Existence of Planning Horizons," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 391-401, August.
    3. Irwin E. Schochetman & Robert L. Smith, 1989. "Infinite Horizon Optimization," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 559-574, August.
    4. Huang, Kai & Ahmed, Shabbir, 2010. "A stochastic programming approach for planning horizons of infinite horizon capacity planning problems," European Journal of Operational Research, Elsevier, vol. 200(1), pages 74-84, January.
    5. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
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