Empirical Estimates via Stability in Stochastic Programming

0098139 - ÚTIA 2008 CZ eng V - Výzkumná zpráva
Kaňková, Vlasta
Empirical Estimates via Stability in Stochastic Programming.
[Empirické odhady a stabilita ve stochastickém programování.]
Praha: ÚTIA AV ČR, 2007. 25 s. Research Report, 2192.
Grant CEP: GA ČR(CZ) GA402/06/1417; GA ČR GA402/05/0115; GA ČR GA402/07/1113
Výzkumný záměr: CEZ:AV0Z10750506
Klíčová slova: Stochastic programming * stability * Wasserstein metric * empirical estimates * convergence rate * problems with penalty and recourse * integer simple recourse case * resk funkcionals
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum

It is known that optimization problems depending on a probability measure correspond to many applications. It is also known that these problems belong mostly to a class of nonlinear optimization problems and, moreover, that very often an ``underlying" probability measure is not completely known. The aim of the research report is to deal with the case when an empirical measure substitutes the theoretical one. In particular, the aim is to generalize reults dealing with convergence rate in the case of empirical esrimates. The introduced results are based on the stability results corresponding to the Wasserstein metric. A relationship berween tails of one-dimensional marginal distribution functions and exponentional rate of convergence are introduced. The corresponding results are focus mainly on ``classical" type of problems corresponding to the cases with penalty and recourse. However, an integer simple recourse case and some special risk funkcionals are discussed also.
Trvalý link: http://hdl.handle.net/11104/0157128