Valid Linear Programming Bounds for Exact Mixed-Integer Programming

References

• Achterberg T. Constraint integer programming. (2007) . Ph.D. thesis, Tehnische universität, BerlinGoogle Scholar
• Achterberg T. SCIP: Solving constraint integer programs. Math. Programming Comput. (2009) 1(1):1–41Crossref, Google Scholar
• Achterberg T, Koch T, Martin A. MIPLIB 2003. Oper. Res. Lett. (2006) 34(4):361–372Crossref, Google Scholar
• Althaus E, Dumitriu D, Vahrenhold J. Fast and accurate bounds on linear programs. Proc. Eighth Internat. Sympos. Experiment. Algorithms (SEA 2009) (2009) 5526:40–50Crossref, Google Scholar
• Applegate DL, Bixby RE, Chvátal V, Cook WJ. The Traveling Salesman Problem: A Computational Study (2006) (Princeton University Press, Princeton, NJ) Google Scholar
• Applegate DL, Cook WJ, Dash S, Espinoza DG. Exact solutions to linear programming problems. Oper. Res. Lett. (2007a) 35(6):693–699Crossref, Google Scholar
• Applegate DL, Cook WJ, Dash S, Espinoza DG. QSopt_ex. (2007b) . Accessed March 2012, http://www.dii.uchile.cl/~daespino/ESolver_doc/main.htmlGoogle Scholar
• Bixby RE, Ceria S, McZeal CM, Savelsbergh MWP. An updated mixed integer programming library: MIPLIB 3.0. Optima (1998) 58:12–15Google Scholar
• Cook WJ, Koch T, Steffy DE, Wolter K, Günlük O, Woeginger G. An exact rational mixed-integer programming solver. Integer Programming and Combinatoral Optimization, LNCS (2011) 6655(Springer-Verlag, Berlin, Heidelberg) 104–116Crossref, Google Scholar
• Dash S, Goycoolea M. A heuristic to generate rank-1 GMI cuts. Math. Programming Comput. (2010) 2(3-4):231–257Crossref, Google Scholar
• Dhiflaoui M, Funke S, Kwappik C, Mehlhorn K, Seel M, Schömer E, Schulte R, Weber D. Certifying and repairing solutions to large LPs: How good are LP-solvers? Proc. Fourteenth Annual ACM-SIAM Sympos. Discrete Algorithms (SODA 2003) (2003) (SIAM, Philadelphia) 255–256Google Scholar
• Dolan ED, Moré JJ. Benchmarking optimization software with performance profiles. Math. Programming (2001) 91(2):201–213Crossref, Google Scholar
• Espinoza DG. On linear programming, integer programming and cutting planes. (2006) . Ph.D. thesis, School of Industrial and Systems Enginerring, Georgia Institute of Technology, AtlantaGoogle Scholar
• Freund RM, Roundy R, Todd MJ. Identifying the set of always-active constraints in a system of linear inequalities by a single linear program. Tech. Rep. (1985) (Sloan School of Management, MIT) Google Scholar
• GMP GNU multiple precision arithmetic library, version 4.3. (2009) . Accessed March 2012, http://gmplib.orgGoogle Scholar
• IBM ILOG CPLEX. (2011) . Accessed March 2012, http://www.ilog.com/products/cplexGoogle Scholar
• Jansson C. Rigorous lower and upper bounds in linear programming. SIAM J. Optim. (2004) 14(3):914–935Crossref, Google Scholar
• Keil C, Jansson C. Computational experience with rigorous error bounds for the NETLIB linear programming library. Reliable Comput. (2006) 12(4):303–321Crossref, Google Scholar
• Koch T. The final NETLIB-LP results. Oper. Res. Lett. (2004) 32(2):138–142Crossref, Google Scholar
• Kwappik C. Exact Linear Programming. (1998) . Master's thesis, Universität des Saarlandes, Saarbrücken, GermanyGoogle Scholar
• Mittelmann HD. Benchmarks for Optimization Software. (2010) . Accessed March 2012, http://plato.asu.edu/bench.htmlGoogle Scholar
• Neumaier A, Shcherbina O. Safe bounds in linear and mixed-integer linear programming. Math. Programming (2004) 99(2):283–296Crossref, Google Scholar
• Steffy DE. Topics in exact precision mathematical programming. (2011) . Ph.D. thesis, Algorithms, Combinatorics and Optimization, Georgia Institute of Technology, AtlantaGoogle Scholar
• Suhl UH, Suhl LM. Computing sparse LU factorizations for large-scale linear programming bases. ORSA J. Comput. (1990) 2(4):325–335Link, Google Scholar