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

Authors:
A. I. Kibzun;A. V. Naumov;V. I. Norkin
Affiliations:
Moscow State Aviation Institute, Moscow, Russia;Moscow State Aviation Institute, Moscow, Russia;V.M. Glushkov Institute of Cybernetics, National Academy of Sciences, Kiev, Ukraine
Venue:
Automation and Remote Control
Year:
2013

Citing 4
Cited 1

An integer programming approach for linear programs with probabilistic constraints

Mathematical Programming: Series A and B
Algorithm to optimize the quantile criterion for the polyhedral loss function and discrete distribution of random parameters

Automation and Remote Control
On the two-stage problem of linear stochastic programming with quantile criterion and discrete distribution of the random parameters

Automation and Remote Control
Relaxations for probabilistically constrained programs with discrete random variables

Operations Research Letters

Bilevel stochastic linear programming problems with quantile criterion

Automation and Remote Control

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.