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A lifted linear programming branch-and-bound algorithm for mixed integer conic quadratic programs (2007)
| Citations: | 26 - 1 self |
BibTeX
@TECHREPORT{Vielma07alifted,
author = {Juan Pablo Vielma and Shabbir Ahmed and George L. Nemhauser},
title = {A lifted linear programming branch-and-bound algorithm for mixed integer conic quadratic programs},
institution = {},
year = {2007}
}
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Abstract
This paper develops a linear programming based branch-and-bound algorithm for mixed in-teger conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from other linear programming based branch-and-bound algo-rithms for mixed integer nonlinear programs in that, it is not based on cuts from gradient inequalities and it sometimes branches on integer feasible solutions. The algorithm is tested on a series of portfolio optimization problems. It is shown that it significantly outperforms commercial and open source solvers based on both linear and nonlinear relaxations. Key words: nonlinear integer programming; branch and bound; portfolio optimization History: February 2007. 1.
Keyphrases
branch-and-bound algorithm mixed integer conic quadratic program polyhedral relaxation integer feasible solution branch-and-bound algo-rithms linear programming portfolio optimization history nonlinear integer programming key word portfolio optimization problem nonlinear relaxation mixed in-teger conic quadratic program conic quadratic constraint mixed integer nonlinear program open source solver gradient inequality
