Abstract
We present computational experience with a branch-and-cut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in financial applications. The algorithm solves the largest real-life problems in a few minutes of run-time.
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References
E. Balas, Intersection cuts—a new type of cutting planes for integer programming.Operations Research 19 (1971) 19–39.
E. Balas, S. Ceria and G. Cornuéjols. A lift-and-project cutting plane algorithm for mixed 0–1 programs,Mathematical Programming 58 (1993) 295–324.
E. Balas, S. Ceria and G. Cornuéjols. Mixed 0–1 programming by lift-and-project in a branch-and-cut framework,Management Science (to appear).
W. Cook, personal communication.
R. Bixby, personal communication.
R. Bixby, W.J. Cook, A. Cox and E. Lee, Parallel mixed-integer programming, manuscript (1994).
Cplex Optimization, Inc.
J. Eckstein, Parallel branch-and-bound algorithms for general mixed integer programming on the CM-5,SIAM Journal on Optimization 4 (1994) 794–814.
R. Fletcher,Practical Methods of Optimization, Vol. 2 (Wiley, 1981).
H. Konno and K. Suzuki, A fast algorithm for solving large scale mean-variance models by compact factorization of covariance matrices, Report IHSS 91-32, Institute of Human and Social Sciences, Tokyo Institute of Technology (1991).
G.L. Nemhauser and L.A. Wolsey,Integer and Combinatorial Optimization (Wiley, New York, 1988).
D.G. Luenberger,Linear and Nonlinear Programming (Addison Wesley, 1984).
A.F. Perold, Large-scale protfolio optimization,Management Science 30 (1984) 1143–1160.
M. Savelsbergh, personal communication (1995).
L.A. Wolsey, personal communication.
R.J. Vanderbei and T.J. Carpenter, Symmetric indefinite systems for interior point methods,Mathematical Programming 58 (1993) 1–32.
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Bienstock, D. Computational study of a family of mixed-integer quadratic programming problems. Mathematical Programming 74, 121–140 (1996). https://doi.org/10.1007/BF02592208
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DOI: https://doi.org/10.1007/BF02592208