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SPEPS Preprint

Author(s): Yu. Nesterov, CORE, Catholic University of Louvain, Louvain-la-Neuve
J.-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
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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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