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Asymptotic sign-solvability, multiple objective linear programming, and the nonsubstitution theorem

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  • L. Cayton
  • R. Herring
  • A. Holder
  • J. Holzer
  • C. Nightingale
  • T. Stohs

Abstract

In this paper we investigate the asymptotic stability of dynamic, multiple-objective linear programs. In particular, we show that a generalization of the optimal partition stabilizes for a large class of data functions. This result is based on a new theorem about asymptotic sign-solvable systems. The stability properties of the generalized optimal partition are used to address a dynamic version of the nonsubstitution theorem. Copyright Springer-Verlag 2006

Suggested Citation

  • L. Cayton & R. Herring & A. Holder & J. Holzer & C. Nightingale & T. Stohs, 2006. "Asymptotic sign-solvability, multiple objective linear programming, and the nonsubstitution theorem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 541-555, December.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:3:p:541-555
    DOI: 10.1007/s00186-006-0095-z
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    References listed on IDEAS

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    1. Eitan Altman & Konstantin E. Avrachenkov & Jerzy A. Filar, 1999. "Asymptotic linear programming and policy improvement for singularly perturbed Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 97-109, March.
    2. Parkash Chander, 1974. "A Simple Proof of the Nonsubstitution Theorem," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(4), pages 698-701.
    3. Kurz,Heinz D. & Salvadori,Neri, 1995. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521443258.
    4. Kurz,Heinz D. & Salvadori,Neri, 1997. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521588676.
    5. Caron, Richard J. & Greenberg, Harvey J. & Holder, Allen G., 2002. "Analytic centers and repelling inequalities," European Journal of Operational Research, Elsevier, vol. 143(2), pages 268-290, December.
    6. Kuga, K., 2001. "The Non-Substitution Theorem: Multiple Primary Factors and the Cost Function Approach," ISER Discussion Paper 0529, Institute of Social and Economic Research, Osaka University.
    7. J. A. Mirrlees, 1969. "The Dynamic Nonsubstitution Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(1), pages 67-76.
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