A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse

We introduce stochastic integer programs with second-order dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-st...

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Bibliographic Details
Published in:Mathematical programming Vol. 126; no. 1; pp. 179 - 190
Main Authors: Gollmer, Ralf, Gotzes, Uwe, Schultz, Rüdiger
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.01.2011
Springer
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Blocking
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Distribution theory
Dominance
Equivalence
Exact sciences and technology
Full Length Paper
Integer programming
Integers
Linear programming
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Optimization
Perturbation methods
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Statistics
Stochastic models
Stochasticity
Studies
Theoretical
60E15
Stochastic dominance
90C15
Stochastic integer programming
90C11
Mixed-integer optimization
Structured programming
Partial ordering
Mixed integer programming
Probability distribution
Set constraint
Modeling
Optimization
Stochastic programming
Integer programming
Ordering
Large scale
Test power
Probability measure
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Description
Summary:We introduce stochastic integer programs with second-order dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed- integer linear programming equivalents to the dominance constrained stochastic programs are identified. For these models, a decomposition algorithm is proposed and tested with instances from power optimization.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-009-0270-0