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

Andrey Kibzun (kibzun***at***mail.ru)
Andrey Naumov (naumovav***at***mail.ru)
Vladimir Norkin (norkin***at***ipnet.kiev.ua)

Abstract: We suggest a method for equivalent transformation of a quantile optimization problem with discrete distribution of random parameters to mixed integer programming problems. The number of additional integer (in fact boolean) variables in the equivalent problems equals to the number of possible scenarios for random data. The obtained mixed integer problems are solved by standard discrete optimization software. Applications to financial portfolio optimization are considered. Results of a numerical experiment are presented.

Keywords: Stochastic programming, quantile optimization, chance constraints, discrete distribution, deterministic equivalent, mixed integer problem.

Category 1: Stochastic Programming

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Applications -- OR and Management Sciences (Finance and Economics )

Citation: Kibzun, A.I., Naumov, A.V., and Norkin, V.I.On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem // Automation and Remote Control. June 2013, Volume 74, Issue 6, pp 951-967

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Entry Submitted: 04/09/2013
Entry Accepted: 04/09/2013
Entry Last Modified: 09/27/2013

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