Duality Gaps in Stochastic Integer Programming

  • Authors:

  • Suvrajeet Sen;Julia L. Higle;John R. Birge

  • Affiliations:

  • Department of Systems and Industrial Engineering, The University of Arizona, Tucson, AZ 85721, USA/;Department of Systems and Industrial Engineering, The University of Arizona, Tucson, AZ 85721, USA/;McCormick School of Engineering and Applied Science, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2000

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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.