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SPEPS Preprint

 Author(s): Yu. Nesterov, CORE, Catholic University of Louvain, Louvain-la-NeuveJ.-Ph. Vial, HEC, University of Geneva, Geneva Title: Confidence level solutions for stochastic programming Date of Acceptance: 07.04.2000 Submission Date: 14.02.2000 Series Title: Stochastic Programming E-Print Series (SPEPS) Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen Complete Preprint: pdf (urn:nbn:de:kobv:11-10057628) Keywords (eng): Stochastic programming, Stochastic subgradient, Complexity estimate Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link. Endnote   Bibtex print on demand: If you click on this icon you can order a print copy of this publication. Diese Seite taggen: These icons lead to social bookmarking systems where you can create and manage personal bookmarks and discover bookmakrs of other users.

Abstract (eng):
We propose an alternative approach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable. The associated objective value is doubly random, since it depends on two outcomes: the event in the stochastic program and the randomized algorithm. We propose a solution concept in which the probability that the randomized algorithm produces a solution with an expected objective value departing from the optimal one by more than $\epsilon$ is small enough. We derive complexity bounds for this process. We show that by repeating the basic process on independent sample, one can significantly sharpen the complexity bounds.
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