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Statistical verification of optimality conditions for stochastic programs with recourse

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Abstract

Statistically motivated algorithms for the solution of stochastic programming problems typically suffer from their inability to recognize optimality of a given solution algorithmically. Thus, the quality of solutions provided by such methods is difficult to ascertain. In this paper, we develop methods for verification of optimality conditions within the framework of Stochastic Decomposition (SD) algorithms for two stage linear programs with recourse. Consistent with the stochastic nature of an SD algorithm, we provide termination criteria that are based on statistical verification of traditional (deterministic) optimality conditions. We propose the use of “bootstrap methods” to confirm the satisfaction of generalized Kuhn-Tucker conditions and conditions based on Lagrange duality. These methods are illustrated in the context of a power generation planning model, and the results are encouraging.

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Authors and Affiliations

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

    Julia L. Higle & Suvrajeet Sen

Authors
  1. Julia L. Higle
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  2. Suvrajeet Sen
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Additional information

This work was supported in part by Grant No. AFOSR-88-0076 from the Air Force Office of Scientific Research and Grant No. DDM-89-10046 from the National Science Foundation.

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Higle, J.L., Sen, S. Statistical verification of optimality conditions for stochastic programs with recourse. Ann Oper Res 30, 215–239 (1991). https://doi.org/10.1007/BF02204818

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