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Statistical Inference of Stochastic Optimization Problems

  • Alexander Shapiro
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 49)

Abstract

We discuss in this paper statistical inference of Monte Carlo simulation based approximations of stochastic optimization problems, where the “true” objective function, and probably some of the constraints, are estimated, typically by averaging a random sample. The classical maximum likelihood estimation can be considered in that framework. Recently statistical analysis of such methods has been motivated by a development of simulation based optimization techniques. We investigate asymptotic properties of the optimal value and an optimal solution of the corresponding Monte Carlo simulation approximations by employing the so-called Delta method, and discuss some examples.

Keywords

Stochastic Programming Random Element Order Expansion Unique Optimal Solution True Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Alexander Shapiro
    • 1
  1. 1.Georgia Institute of TechnologyAtlantaUSA

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