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Nonanticipativity and L 1-martingales in stochastic optimization problems

  • Optimization
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Stochastic Systems: Modeling, Identification and Optimization, II

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 6))

Abstract

Necessary and sufficient conditions for optimality are derived for multistage stochastic programs. In particular it is shown that under some standard regularity conditions and a condition of “nonanticipative feasibility”, a system of Lagrange multipliers, characterized by a martingale property, can be associated with the constraints of the problem. Nonanticipative feasibility is expressed in terms of the nonanticipativity of a certain multifunction and is shown to be related to the more familiar concept—in stochastic programming—of relatively complete recourse. It is also shown that this restriction renders possible the justification of the dynamic programming technique.

Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under AFOSR Grant Number 72-2269

Supported in part by the National Science Foundation under grant MPS 75-07028

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Authors and Affiliations

  1. University of Washington, Seattle, Wash., USA

    R. T. Rockafellar

  2. University of Kentucky, Lexington, Ky., USA

    R. J.-B. Wets

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  1. R. T. Rockafellar
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  2. R. J.-B. Wets
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Roger J.- B. Wets

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© 1976 The Mathematical Programming Society

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Rockafellar, R.T., Wets, R.JB. (1976). Nonanticipativity and L 1-martingales in stochastic optimization problems. In: Wets, R.J.B. (eds) Stochastic Systems: Modeling, Identification and Optimization, II. Mathematical Programming Studies, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120750

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  • DOI: https://doi.org/10.1007/BFb0120750

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00785-9

  • Online ISBN: 978-3-642-00786-6

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