A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs

Authors:
Juan Pablo Vielma;Shabbir Ahmed;George L. Nemhauser
Affiliations:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Venue:
INFORMS Journal on Computing
Year:
2008

Citing 0
Cited 5

An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints

Operations Research
Branching and bounds tighteningtechniques for non-convex MINLP

Optimization Methods & Software - GLOBAL OPTIMIZATION
An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application

Operations Research
A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes

Operations Research Letters
Communication: On families of quadratic surfaces having fixed intersections with two hyperplanes

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper develops a linear-programming-based branch-and-bound algorithm for mixed-integer conic quadratic programs. The algorithm is based on a known higher-dimensional or lifted polyhedral relaxation of conic quadratic constraints. The algorithm is different from other linear-programming-based branch-and-bound algorithms 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.