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

References

• Abhishek K., Leyffer S., Linderoth J. T. Filmint: An outer-approximation-based solver for nonlinear mixed integer programs. (2006) . Preprint ANL/MCS-P1374-0906, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, ILGoogle Scholar
• Akturk M. S., Atamturk A., Gurel S. A strong conic quadratic reformulation for machine-job assignment with controllable processing times. Optimization Online (2007) . http://www.optimization-online.org/DB_HTML/2007/06/1698.htmlGoogle Scholar
• Ball K. M., Levy S. An elementary introduction to modern convex geometry. Flavors of Geometry, Mathematical Sciences Research Institute Publications (1997) 31(Cambridge University Press, New York) 1–58Google Scholar
• Ben-Tal A., Nemirovski A. Robust solutions of uncertain linear programs. Oper. Res. Lett. (1999) 25:1–13Crossref, Google Scholar
• Ben-Tal A., Nemirovski A.Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (2001a) (Society for Industrial and Applied Mathematics, Philadelphia) Crossref, Google Scholar
• Ben-Tal A., Nemirovski A. On polyhedral approximations of the second-order cone. Math. Oper. Res. (2001b) 26:193–205Link, Google Scholar
• Bertsimas D., Shioda R. An algorithm for cardinality constrained quadratic optimization problems. (2004) . Working paper, MIT, Cambridge, MA, http://web.mit.edu/dbertsim/www/papers.htmlGoogle Scholar
• Bienstock D. Computational study of a family of mixed-integer quadratic programming problems. Math. Programming (1996) 74:121–140Crossref, Google Scholar
• Bonami P., Waechter A., Biegler L. T., Conn A. R., Cornuejols G., Grossmann I. E., Laird C. D., Lee J., Lodi A., Margot F., Sawaya N. An algorithmic framework for convex mixed integer nonlinear programs. (2005) . IBM Research Report RC23771, IBM, Yorktown Heights, NYGoogle Scholar
• Borchers B., Mitchell J. E. An improved branch and bound algorithm for mixed integer nonlinear programs. Comput. Oper. Res. (1994) 21:359–367Crossref, Google Scholar
• Ceria S., Stubbs R. A. Incorporating estimation errors into portfolio selection: Robust portfolio construction. J. Asset Management (2006) 7:109–127Crossref, Google Scholar
• Chang T.-J., Meade N., Beasley J. E., Sharaiha Y. M. Heuristics for cardinality constrained portfolio optimisation. Comput. Oper. Res. (2000) 27:1271–1302Crossref, Google Scholar
• Dolan E. D., Moré J. J. Benchmarking optimization software with performance profiles. Math. Programming (2002) 91:201–213Crossref, Google Scholar
• Duran M. A., Grossmann I. E. An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Programming (1986) 36:307–339Crossref, Google Scholar
• Fletcher R., Leyffer S. Solving mixed integer nonlinear programs by outer approximation. Math. Programming (1994) 66:327–349Crossref, Google Scholar
• Geoffrion A. Generalized Benders decomposition. J. Optim. Theory Appl. (1972) 10:237–260Crossref, Google Scholar
• Glineur F. Computational experiments with a linear approximation of second order cone optimization. (2000) . Image Technical Report 0001, Service de Mathématique et de Recherche Opérationnelle, Faculté Polytechnique de Mons, Mons, BelgiumGoogle Scholar
• Grossmann I. E. Review of nonlinear mixed-integer and disjunctive programming techniques. Optim. Engrg. (2002) 3:227–252Crossref, Google Scholar
• Gupta O. K., Ravindran A. Branch and bound experiments in convex nonlinear integer programming. Management Sci. (1985) 31:1533–1546Link, Google Scholar
• Horst R., Pardalos P. M., Thoai N. V.Introduction to Global Optimization, Nonconvex Optimization and Its Applications (1995) 3(Kluwer Academic Publishers, Dordrecht, The Netherlands) Google Scholar
• ILOGCplex 10: User's Manual and Reference Manual (2005) (ILOG, Mountain View, CA) Google Scholar
• Leyffer S. Integrating SQP and branch-and-bound for mixed integer nonlinear programming. Comput. Optim. Appl. (2001) 18:295–309Crossref, Google Scholar
• Lobo M. S., Fazel M., Boyd S. Portfolio optimization with linear and fixed transaction costs. Ann. Oper. Res. (2007) 152:341–365Crossref, Google Scholar
• Lobo M. S., Vandenberghe L., Boyd S. Application of second-order cone programming. Linear Algebra Appl. (1998) 284:193–228Crossref, Google Scholar
• Maringer D., Kellerer H. Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectrum (2003) 25:481–495Crossref, Google Scholar
• Quesada I., Grossmann I. E. An LP/NLP based branch and bound algorithm for convex MINLP optimization problems. Comput. Chem. Engrg. (1992) 16:937–947Crossref, Google Scholar
• Stubbs R. A., Mehrotra S. A branch-and-cut method for 0-1 mixed convex programming. Math. Programming (1999) 86:515–532Crossref, Google Scholar
• Tawarmalani M., Sahinidis N. V. Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Math. Programming (2004) 99:563–591Crossref, Google Scholar
• Westerlund T., Pettersson F. An extended cutting plane method for solving convex MINLP problems. Comput. Chem. Engrg. (1995) 19:S131–S136Crossref, Google Scholar
• Westerlund T., Pettersson F., Grossmann I. E. Optimization of pump configurations as a MINLP problem. Comput. Chem. Engrg. (1994) 18:845–858Crossref, Google Scholar