Abstract

A standard approach to duality in stochastic optimization problems with constraints in L∞L_{\infty} relies upon the Yosida - Hewitt theorem. We develop an alternative technique which employs only "elementary" means. The technique is based on an ε\varepsilon-regularization of the original problem and on passing to the limit as ε→0\varepsilon \to 0 with the help of a simple measure-theoretic fact – the biting lemma.

Author information

Contact details are reproduced from the original publication and may be historical.

Igor V. Evstigneev

School of Economic Studies, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain

igor.evstigneev@man.ac.uk

Sjur D. Flåm

Dept. of Economics, University of Bergen, Fosswinckels gate 6, 5007 Bergen, Norway

sjur.flaam@econ.uib.no

Keywords

  • Stochastic optimization
  • convex duality
  • constraints in L-infinity
  • stochastic Lagrange multipliers
  • bounded sets in L-1
  • biting lemma
  • Gale's economic model

Mathematics Subject Classification

90C15, 51A41; 90C19, 90A16

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Suggested citation

I. V. Evstigneev, S. D. Flåm. “Convex Stochastic Duality and the "Biting Lemma".” Journal of Convex Analysis 9 (2002), No. 1, 237–244. https://doi.org/10.68381/jca09011

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press LLC.