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Duality Gaps in Stochastic Integer Programming

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Abstract

In this note, we explore the implications of a result that suggests that the duality gap caused by a Lagrangian relaxation of the nonanticipativity constraints in a stochastic mixed integer (binary) program diminishes as the number of scenarios increases. By way of an example, we illustrate that this is not the case. In general, the duality gap remains bounded away from zero.

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Authors and Affiliations

  1. Department of Systems and Industrial Engineering, The University of Arizona, Tucson, AZ, 85721, USA

    Suvrajeet Sen & Julia L. Higle

  2. McCormick School of Engineering and Applied Science, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, 60208, USA

    John R. Birge

Authors
  1. Suvrajeet Sen
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  2. Julia L. Higle
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  3. John R. Birge
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Sen, S., Higle, J.L. & Birge, J.R. Duality Gaps in Stochastic Integer Programming. Journal of Global Optimization 18, 189–194 (2000). https://doi.org/10.1023/A:1008314824754

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  • DOI: https://doi.org/10.1023/A:1008314824754

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