On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem

We propose an equivalent reduction of the quantile optimization problem with a discrete distribution of random parameters to a partially integer programming problem of large dimension. The number of integer (Boolean) variables in this problem equals the number of possible values for the random param...

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Bibliographic Details
Published in:Automation and remote control Vol. 74; no. 6; pp. 951 - 967
Main Authors: Kibzun, A. I., Naumov, A. V., Norkin, V. I.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01.06.2013
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Computer programs
Computer-Aided Engineering (CAD
Control
Equivalence
Integer programming
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Optimization
Quantiles
Queueing Systems
Robotics
Stochastic Systems
Systems Theory
Vectors (mathematics)
Stochastic Program
Discrete Distribution
Quantile Function
Boolean Variable
Remote Control
ISSN:0005-1179, 1608-3032
Online Access:Get full text
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Summary:We propose an equivalent reduction of the quantile optimization problem with a discrete distribution of random parameters to a partially integer programming problem of large dimension. The number of integer (Boolean) variables in this problem equals the number of possible values for the random parameters vector. The resulting problems can be solved with standard discrete optimization software. We consider applications to quantile optimization of a financial portfolio and show results of numerical experiments.
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ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117913060064