An Ergodic Theorem for Random Lagrangians with an Application to Stochastic Programming

Adib Bagh; Michael Casey

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SPEPS Preprint

Author(s):	Adib Bagh, University of California, Davis Michael Casey, University of Puget Sound, Tacoma
Title:	An Ergodic Theorem for Random Lagrangians with an Application to Stochastic Programming
Date of Acceptance:	21.07.2003
Submission Date:	20.07.2003
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10059143)
Keywords (eng):	stochastic programming, duality, saddle point, ergodic theory, lagrangian, epi/hyo-convergence
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Abstract (eng):

We prove an ergodic theorem showing the almost sure epi/hypo-convergence of a sequence of random lagrangians to a limit lagrangian where the random lagrangians are generated by stationary sampling of a probability measure. We apply this theorem to stochastic programming and demonstrate that the outer set-limit of the sequence of the set of saddle points from the sampled problems is a subset of the set of saddle points of the true problem.

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