Generalized bounds for convex multistage stochastic programs

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Generalized bounds for convex multistage stochastic programs Daniel Kuhn
Type:	eBook
Released:	2004
Publisher:	Springer
Page Count:	199
Format:	djvu
Language:	English
ISBN-10:	3540225404
ISBN-13:	9783540225409

This book investigates convex multistage stochastic programs whose objective and constraint functions exhibit a generalized nonconvex dependence on the random parameters.Generalized bounds for convex ... Textbook Although the classical Jensen and Edmundson-Madansky type bounds or its extensions are generally not available for such problems, tight bounds can systematically be constructed under mild regularity conditions. A nice primal-dual symmetry property is revealed when the proposed bounding method is applied to linear stochastic programs. After having developed the theoretical concepts, exemplary real-life applications are studied. It is shown how market power, lognormal stochastic processes, and risk-aversion can be properly handled in a stochastic programming framework. Numerical experiments show that the relative gap between the bounds can be reduced to a few percent without exploding the problem size.