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Computational complexity of stochastic programming problems

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An Erratum to this article was published on 17 July 2015

Abstract

Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast quantity of literature on the subject has appeared. Developments in the theory of computational complexity allow us to establish the theoretical complexity of a variety of stochastic programming problems studied in this literature. Under the assumption that the stochastic parameters are independently distributed, we show that two-stage stochastic programming problems are ♯P-hard. Under the same assumption we show that certain multi-stage stochastic programming problems are PSPACE-hard. The problems we consider are non-standard in that distributions of stochastic parameters in later stages depend on decisions made in earlier stages.

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Authors and Affiliations

  1. School of Computing, University of Leeds, United Kingdom

    Martin Dyer

  2. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven and CWI, Amsterdam, The Netherlands

    Leen Stougie

Authors
  1. Martin Dyer
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  2. Leen Stougie
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Correspondence to Martin Dyer.

Additional information

Supported by the EPSRC grant ``Phase Transitions in the Complexity of Randomised Algorithms'', by the EC IST project RAND-APX, and by the MRT Network ADONET of the European Community (MRTN-CT-2003-504438).

An erratum to this article is available at http://dx.doi.org/10.1007/s10107-015-0935-9.

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Dyer, M., Stougie, L. Computational complexity of stochastic programming problems. Math. Program. 106, 423–432 (2006). https://doi.org/10.1007/s10107-005-0597-0

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  • DOI: https://doi.org/10.1007/s10107-005-0597-0

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