Why Does Monte Carlo Fail to Work Properly in High-Dimensional Optimization Problems?

Boris Polyak () and Pavel Shcherbakov ()
Additional contact information
Boris Polyak: Institute for Control Sciences, RAS
Pavel Shcherbakov: Institute for Control Sciences, RAS

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 2, No 12, 612-627

Abstract: Abstract The paper presents a quantitative explanation of failure of generic Monte Carlo techniques as applied to optimization problems of high dimensions. Deterministic grids are also discussed.

Keywords: Monte Carlo; Sample size; Accuracy; Linear objective; $$l_p$$ l p -balls; Deterministic grids; 65C05 Monte Carlo methods; 65Kxx Mathematical programming; optimization and variational techniques; 90-08 Computational methods; 90C06 Large-scale problems; 90C29 Multiobjective and goal programming (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-1045-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:173:y:2017:i:2:d:10.1007_s10957-016-1045-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-016-1045-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().