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Approximating infinite horizon stochastic optimal control in discrete time with constraints

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Abstract

Traditional approaches to solving stochastic optimal control problems involve dynamic programming, and solving certain optimality equations. When recast as stochastic programming problems, structural aspects such as convexity are retained, and numerical solution procedures based on decomposition and duality may be exploited. This paper explores a class of stationary, infinite-horizon stochastic optimization problems with discounted cost criterion. Constraints on both states and controls are permitted, and modeled in the objective function by allowing it to take infinite values. Approximating techniques are developed using variational analysis, and intuitive lower bounds are obtained via averaging the future. These bounds could be used in a finite-time horizon stochastic programming setting to find solutions numerically.

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References

  • Bertsekas, D. (1987). “Dynamic Programming: Deterministic and Stochastic Models.” Prentice-Hall, Englewood Cliffs.

    Google Scholar 

  • Durrett, R. (1991). “Probability: Theory and Examples.” Brooks/Cole, Pacific Grove, CA.

    Google Scholar 

  • Flåm, S. and R.J.-B. Wets. (1987). “Existence Results and Finite Horizon Approximates for Infinite Horizon Optimization Problems.” Econometrica 55, 1187–1209.

    Google Scholar 

  • Flåm, S. and R.J-B. Wets. (1986). “Finite Horizon Approximates of in Finite Horizon Stochastic Programs.” Stochastic Optimization. 81, 337–350.

    Google Scholar 

  • Gihman, I.I. and A.V. Skorohod. (1979). “Controlled Stochastic Processes.” Springer-Verlag, New York-Heidelberg.

    Google Scholar 

  • Grinold, R.C. (1977). “Finite Horizon Approximates of Infinite Horizon Linear Programs.” Mathematical Programming 12, 1–17.

    Article  Google Scholar 

  • Hinderer, K.F. (1985). “On the Structure of Solutions of Stochastic Dynamic Programs.” Proceedings of the seventh conference on probability theory, pp. 173–182.

  • Puterman, M. (1994). “Markov Decision Processes: Discrete Stochastic Dynamic Programming.” Wiley, New York.

    Google Scholar 

  • Rieder, U. and R. Zagst. (1994). “Monotonicity and Bounds for Convex Stochastic Control Models.” Z. Oper. Res. 39 (2), 187–207.

    Google Scholar 

  • Rockafellar, R.T. and R.J.-B. Wets. (1998). “Variational Analysis.” Springer-Verlag.

  • Whitt, W. (1978). “Approximations of Dynamic Programs I.” Math. Oper. Res. 3 (3), 231–243.

    Article  Google Scholar 

  • Whitt, W. (1979). “Approximations of Dynamic Programs II.” Math. Oper. Res. 4 (2), 179–185.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Texas, Austin, Texas

    Lisa A. Korf

Authors
  1. Lisa A. Korf
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Correspondence to Lisa A. Korf.

Additional information

Research supported in part by a grant of the National Science Foundation.

AMS Classification 46N10, 49N15, 65K10, 90C15, 90C46

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Korf, L.A. Approximating infinite horizon stochastic optimal control in discrete time with constraints. Ann Oper Res 142, 165–186 (2006). https://doi.org/10.1007/s10479-006-6167-x

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  • DOI: https://doi.org/10.1007/s10479-006-6167-x

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