Conditioning of linear-quadratic two-stage stochastic optimization problems

In this paper a condition number for linear-quadratic two-stage stochastic optimization problems is introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probability distribution the solution set of the problem. Being the outer norm of the Mordukhovich coderivative of th...

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Bibliographic Details
Published in:Mathematical programming Vol. 148; no. 1-2; pp. 201 - 221
Main Authors: Emich, Konstantin, Henrion, René, Römisch, Werner
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2014
Springer Nature B.V
Subjects:
Analysis
Calculus
Calculus of Variations and Optimal Control; Optimization
Chains
Combinatorics
Conditioning
Full Length Paper
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical problems
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Norms
Numerical Analysis
Optimization
Probability distribution
Quadratic programming
Stochastic control theory
Stochasticity
Studies
Theoretical
90C31
Simple recourse
Two-stage linear-quadratic problems
49K40
90C15
Conditioning
Stochastic optimization
Coderivative calculus
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:In this paper a condition number for linear-quadratic two-stage stochastic optimization problems is introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probability distribution the solution set of the problem. Being the outer norm of the Mordukhovich coderivative of this multifunction, the condition number can be estimated from above explicitly in terms of the problem data by applying appropriate calculus rules. Here, a chain rule for the extended partial second-order subdifferential recently proved by Mordukhovich and Rockafellar plays a crucial role. The obtained results are illustrated for the example of two-stage stochastic optimization problems with simple recourse.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0734-0