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A dual solution procedure for quadratic stochastic programs with simple recourse

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Numerical Methods

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1005))

Abstract

We exhibit a dual of a stochastic program with simple recourse — with random parameters in the technoloty matrix and the right-hand sides, and with quadratic recourse costs — that is essentially a deterministic quadratic program except for some simple stochastic upper bounds. We then describe a solution procedure for problems of this type based on a finite element representation of the dual variables.

Supported by the Air Force Office of Scientific Research under grant F49620-82-K-0012

Supported in part by a Guggenheim Fellowship

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References

  1. D. Walkup and R. Wets, Stochastic programs with recourse: special forms, in Proceeding of the Princeton Symposium on Mathematical Programming, ed. H. Kuhn, Princeton Univ. Press, Princeton, 1970.

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  2. R. Wets, Solving stochastic programs with simple recourse, Stochastics, (1983).

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  3. R.T. Rockafellar and R. Wets, The optimal recourse problem in discrete time: L1-multipliers for inequality constraints, SIAM J. Control Optim., 16 (1978), 16–36.

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  4. J.-P. Aubin, Mathematical Methods of Game and Economic Theory, North Holland, Amsterdam, 1979.

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  5. R. Wets, Induced constraints for stochastic optimization problems, in Techniques of Optimization, ed. A. Balakrishnan, Academic Press, 1972, 433–443.

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  6. B. Murtagh and M. Saunders, Large-scale linearly constrained optimization, Mathematical Programming, 14 (1978), 41–72.

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  7. M. Frank and P. Wolf, An algorithm for quadratic programming, Naval Res. Logist. Quest. 3 (1956), 95–110.

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Authors and Affiliations

  1. Depart. Mathematics, Univ. Washington, USA

    R. T. Rockafellar

  2. I.I.A.S.A., Laxenburg, USA

    Roger J-B. Wets

Authors
  1. R. T. Rockafellar
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  2. Roger J-B. Wets
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© 1983 Springer-Verlag

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Rockafellar, R.T., Wets, R.JB. (1983). A dual solution procedure for quadratic stochastic programs with simple recourse. In: Numerical Methods. Lecture Notes in Mathematics, vol 1005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0112539

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  • DOI: https://doi.org/10.1007/BFb0112539

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12334-7

  • Online ISBN: 978-3-540-40967-0

  • eBook Packages: Springer Book Archive

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