The Chvátal-Gomory Closure of a Strictly Convex Body

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, Argonne National Laboratory, Mathematics and Computer Science Division, Argonne, ILGoogle Scholar
• Atamtürk A., Narayanan V. The submodular knapsack polytope. Discrete Optim. (2009) 6(4):333–344Crossref, Google Scholar
• Atamtürk A., Narayanan V. Conic mixed-integer rounding cuts. Math. Programming (2010) 122(1):1–20Crossref, Google Scholar
• Atamtürk A., Narayanan V. Lifting for conic mixed-integer programming. Math. Programming Ser. B (2011) 126(2):351–363Crossref, Google Scholar
• Bonami P., Kilinç M., Linderoth J. Algorithms and software for convex mixed integer nonlinear programs. (2009) . Technical Report 1664, Computer Sciences Department, University of Wisconsin–Madison, MadisonGoogle Scholar
• Bonami P., Biegler L. T., Conn A. R., Cornuéjols G., Grossmann I. E., Laird C. D., Lee J., et al. An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optim. (2008) 5(2):186–204Crossref, Google Scholar
• Ceria S., Soares J. Convex programming for disjunctive convex optimization. Math. Programming (1999) 86(3):595–614Crossref, Google Scholar
• Çezik M. T., Iyengar G. Cuts for mixed 0-1 conic programming. Math. Programming (2005) 104(1):179–202Crossref, Google Scholar
• Chvátal V. Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Math. (1973) 4(4):305–337Crossref, Google Scholar
• Cook W. J., Cunningham W. H., Pulleyblank W. R., Schrijver A.Combinatorial Optimization (1998) (John Wiley & Sons, Inc., New York) Google Scholar
• Cornuejols G., Conforti M., Zambelli G., Juerger M., Liebling T., Naddef D., Pulleyblank W., Reinelt D., Rinaldi D., Wolsey L. Polyhedral approaches to mixed integer linear programming. 50 Years of Integer Programming 1958–2008 (2010) (Springer-Verlag, Berlin, Heidelberg) 343–386Google Scholar
• Dey S. S., Vielma J. P., Eisenbrand F., Shepherd F. B. The Chvátal-Gomory closure of an ellipsoid is a polyhedron. Proc. 14th Conf. Integer Programming Combinatorial Optim. (IPCO 2010), Vol. 6080 (2010) (Springer, New York) 327–340Lecture Notes in Computer Science http://www.pitt.edu/∼jvielma/publications/#CG_IPCO_10Crossref, Google Scholar
• Edmonds J. Paths, trees, and flowers. Canadian J. Math. (1965) 17:449–467Crossref, Google Scholar
• Frangioni A., Gentile C. Perspective cuts for a class of convex 0-1 mixed integer programs. Math. Programming (2006) 106(2):225–236Crossref, Google Scholar
• Gomory R. E. An algorithm for integer solutions to linear programs. Recent Advances in Mathematical Programming. (1963) (McGraw-Hill, New York) 269–302Google Scholar
• Gomory R. E. Outline of an algorithm for integer solutions to linear programs. Bull. Amer. Math. Soc. (1958) 64(5):275–278Crossref, Google Scholar
• Grossmann I. E., Lee S. Generalized convex disjunctive programming: Nonlinear convex hull relaxation. Comput. Optim. Appl. (2003) 26(1):83–100Crossref, Google Scholar
• Günlük O., Linderoth J. Perspective relaxation of mixed integer nonlinear programs with indicator variables. Math. Programming, Ser. B (2010) 124(1-2):183–205Crossref, Google Scholar
• Günlük O., Lee J., Weismantel R. MINLP strengthening for separable convex quadratic transportation-cost UFL. (2007) . IBM Research Report RC24213, IBM, Yorktown Heights, NYGoogle Scholar
• Hemmecke R., Köppe M., Lee J., Weismantel R., Juerger M., Liebling T., Naddef D., Pulleyblank W., Reinelt D., Rinaldi D., Wolsey L. Nonlinear integer programming. 50 Years of Integer Programming 1958–2008 (2010) (Springer-Verlag, Berlin, Heidelberg) 561–618Crossref, Google Scholar
• Hiriart-Urruty J.-B., Lemaréchal C.Fundamentals of Convex Analysis (2001) (Springer-Verlag, Berlin, Heidelberg) Crossref, Google Scholar
• Johnson E. L., Nemhauser G. L., Savelsbergh M. W. P. Progress in linear programming-based algorithms for integer programming: An exposition. INFORMS J. Comput. (2000) 12(1):2–23Link, Google Scholar
• Letchford A. N., Sørensen M. M., Lodi A., Panconesi A., Rinaldi G. Binary positive semidefinite matrices and associated integer polytopes. Proc. 13th Internat. Conf. Integer Programming Combinatorial Optim., Vol. 5035 (2008) (Springer-Verlag, Berlin, Heidelberg) 125–139Lecture Notes in Computer ScienceCrossref, Google Scholar
• Leyffer S., Linderoth J. T., Luedtke J., Miller A., Munson T. Applications and algorithms for mixed integer nonlinear programming. J. Phys.: Conf. Ser. (2009) 180(1):012014Crossref, Google Scholar
• Marchand H., Martin A., Weismantel R., Wolsey L. A. Cutting planes in integer and mixed integer programming. Discrete Appl. Math. (2002) 123(1-3):397–446Crossref, Google Scholar
• Nemhauser G. L., Wolsey L. A.Integer and Combinatorial Optimization (1988) (Wiley-Interscience, New York) Crossref, Google Scholar
• Richard J.-P.P., Tawarmalani M. Lifting inequalities: A framework for generating strong cuts for nonlinear programs. Math. Programming (2010) 121(1):61–104Crossref, Google Scholar
• Schrijver A. On cutting planes. Ann. Discrete Math. (1980) 9:291–296Crossref, Google Scholar
• Schrijver A.Theory of Linear and Integer Programming (1986) (John Wiley & Sons, Inc., New York) Google Scholar
• Stubbs R. A., Mehrotra S. A branch-and-cut method for 0-1 mixed convex programming. Math. Programming (1999) 86(3):515–532Crossref, Google Scholar