Conditions for optimality in multi-stage stochastic programming problems: In this paper it is demonstrated how necessary and sufficient conditions for optimality of a strategy in multi-stage stochastic programs may be obtained without topological assumptions. The conditions are essentially based on a dynamic programming approach. These conditions — called conserving and equalizing — show the essential difference between finite-stage and ∞-stage stochastic programs.  Moreover, it is demonstrated how a recursive structure of the problem can give a reformulation of the conditions. These reformulated conditions may be used for the construction of numerical solution techniques.

L.P.J. Groenewegen; J. Wessels

doi:10.1007/978-3-642-51572-9_4

Conditions for optimality in multi-stage stochastic programming problems: In this paper it is demonstrated how necessary and sufficient conditions for optimality of a strategy in multi-stage stochastic programs may be obtained without topological assumptions. The conditions are essentially based on a dynamic programming approach. These conditions — called conserving and equalizing — show the essential difference between finite-stage and ∞-stage stochastic programs. Moreover, it is demonstrated how a recursive structure of the problem can give a reformulation of the conditions. These reformulated conditions may be used for the construction of numerical solution techniques.

L.P.J. Groenewegen, J. Wessels

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Original language	English
Title of host publication	Recent results in stochastic programming (Oberwolfach, Germany, 1979)
Editors	P. Kall, A. Prékopa
Place of Publication	Berlin
Publisher	Springer
Chapter	4
Pages	41-57
Number of pages	17
ISBN (Electronic)	978-3-642-51572-9
ISBN (Print)	978-3-540-10013-3
DOIs	https://doi.org/10.1007/978-3-642-51572-9_4
Publication status	Published - 1980

Publication series

Name	Lecture Notes in Economics and Mathematical Systems
Volume	179
ISSN (Print)	0075-8442

Access to Document

10.1007/978-3-642-51572-9_4

Cite this

Groenewegen, L. P. J., & Wessels, J. (1980). Conditions for optimality in multi-stage stochastic programming problems: In this paper it is demonstrated how necessary and sufficient conditions for optimality of a strategy in multi-stage stochastic programs may be obtained without topological assumptions. The conditions are essentially based on a dynamic programming approach. These conditions — called conserving and equalizing — show the essential difference between finite-stage and ∞-stage stochastic programs. Moreover, it is demonstrated how a recursive structure of the problem can give a reformulation of the conditions. These reformulated conditions may be used for the construction of numerical solution techniques. In P. Kall, & A. Prékopa (Eds.), Recent results in stochastic programming (Oberwolfach, Germany, 1979) (pp. 41-57). (Lecture Notes in Economics and Mathematical Systems; Vol. 179). Springer. https://doi.org/10.1007/978-3-642-51572-9_4

Groenewegen, L.P.J. ; Wessels, J. / Conditions for optimality in multi-stage stochastic programming problems : In this paper it is demonstrated how necessary and sufficient conditions for optimality of a strategy in multi-stage stochastic programs may be obtained without topological assumptions. The conditions are essentially based on a dynamic programming approach. These conditions — called conserving and equalizing — show the essential difference between finite-stage and ∞-stage stochastic programs. Moreover, it is demonstrated how a recursive structure of the problem can give a reformulation of the conditions. These reformulated conditions may be used for the construction of numerical solution techniques. Recent results in stochastic programming (Oberwolfach, Germany, 1979). editor / P. Kall ; A. Prékopa. Berlin : Springer, 1980. pp. 41-57 (Lecture Notes in Economics and Mathematical Systems).

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Groenewegen, LPJ & Wessels, J 1980, Conditions for optimality in multi-stage stochastic programming problems: In this paper it is demonstrated how necessary and sufficient conditions for optimality of a strategy in multi-stage stochastic programs may be obtained without topological assumptions. The conditions are essentially based on a dynamic programming approach. These conditions — called conserving and equalizing — show the essential difference between finite-stage and ∞-stage stochastic programs. Moreover, it is demonstrated how a recursive structure of the problem can give a reformulation of the conditions. These reformulated conditions may be used for the construction of numerical solution techniques. in P Kall & A Prékopa (eds), Recent results in stochastic programming (Oberwolfach, Germany, 1979). Lecture Notes in Economics and Mathematical Systems, vol. 179, Springer, Berlin, pp. 41-57. https://doi.org/10.1007/978-3-642-51572-9_4

Conditions for optimality in multi-stage stochastic programming problems: In this paper it is demonstrated how necessary and sufficient conditions for optimality of a strategy in multi-stage stochastic programs may be obtained without topological assumptions. The conditions are essentially based on a dynamic programming approach. These conditions — called conserving and equalizing — show the essential difference between finite-stage and ∞-stage stochastic programs. Moreover, it is demonstrated how a recursive structure of the problem can give a reformulation of the conditions. These reformulated conditions may be used for the construction of numerical solution techniques. / Groenewegen, L.P.J.; Wessels, J.
Recent results in stochastic programming (Oberwolfach, Germany, 1979). ed. / P. Kall; A. Prékopa. Berlin: Springer, 1980. p. 41-57 (Lecture Notes in Economics and Mathematical Systems; Vol. 179).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Groenewegen LPJ, Wessels J. Conditions for optimality in multi-stage stochastic programming problems: In this paper it is demonstrated how necessary and sufficient conditions for optimality of a strategy in multi-stage stochastic programs may be obtained without topological assumptions. The conditions are essentially based on a dynamic programming approach. These conditions — called conserving and equalizing — show the essential difference between finite-stage and ∞-stage stochastic programs. Moreover, it is demonstrated how a recursive structure of the problem can give a reformulation of the conditions. These reformulated conditions may be used for the construction of numerical solution techniques. In Kall P, Prékopa A, editors, Recent results in stochastic programming (Oberwolfach, Germany, 1979). Berlin: Springer. 1980. p. 41-57. (Lecture Notes in Economics and Mathematical Systems). doi: 10.1007/978-3-642-51572-9_4