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.
Keywords
- Dual Problem
- Stochastic Program
- Dual Variable
- Lagrange Multiplier Vector
- Finite Element Representation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
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.
R. Wets, Solving stochastic programs with simple recourse, Stochastics, (1983).
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.
J.-P. Aubin, Mathematical Methods of Game and Economic Theory, North Holland, Amsterdam, 1979.
R. Wets, Induced constraints for stochastic optimization problems, in Techniques of Optimization, ed. A. Balakrishnan, Academic Press, 1972, 433–443.
B. Murtagh and M. Saunders, Large-scale linearly constrained optimization, Mathematical Programming, 14 (1978), 41–72.
M. Frank and P. Wolf, An algorithm for quadratic programming, Naval Res. Logist. Quest. 3 (1956), 95–110.
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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
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