Essential intersection and approximation results for robust optimization. Hess, C., Seri, R., & Choirat, C. *Journal of Nonlinear and Convex Analysis*, 15(5):979 – 1002, 2014. Paper abstract bibtex We examine the concept of essential intersection of a random set in the framework of robust optimization programs and ergodic theory. Using a recent extension of Birkhoff’s Ergodic Theorem developed by the present authors, it is shown that essential intersection can be represented as the countable intersection of random sets involving an asymptotically mean stationary transformation. This is applied to the approximation of a robust optimization program by a sequence of simpler programs with only a finite number of constraints. We also discuss some formulations of robust optimization programs that have appeared in the literature and we make them more precise, especially from the probabilistic point of view. We show that the essential intersection appears naturally in the correct formulation.

@Article{Hess2014,
Title = {Essential intersection and approximation results for
robust optimization},
Author = {Hess, C. and Seri, R. and Choirat, C.},
Journal = {Journal of Nonlinear and Convex Analysis},
Year = 2014,
Number = 5,
Pages = {979 -- 1002},
Volume = 15,
Abstract = {We examine the concept of essential intersection of
a random set in the framework of robust optimization
programs and ergodic theory. Using a recent
extension of Birkhoff’s Ergodic Theorem developed by
the present authors, it is shown that essential
intersection can be represented as the countable
intersection of random sets involving an
asymptotically mean stationary transformation. This
is applied to the approximation of a robust
optimization program by a sequence of simpler
programs with only a finite number of
constraints. We also discuss some formulations of
robust optimization programs that have appeared in
the literature and we make them more precise,
especially from the probabilistic point of view. We
show that the essential intersection appears
naturally in the correct formulation.},
Url =
{http://www.ybook.co.jp/online2/opjnca/vol15/p979.html}
}

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