Valid linear programming bounds for exact mixed-integer programming

INFORMS Journal on Computing

Volumn 25, Issue 2, 2013, Pages 271-284

  Steffy, Daniel E ^a   Wolter, Kati ^b  

^a OAKLAND UNIVERSITY   (United States)

^b ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Exact computation; Mixed integer programming

Indexed keywords

BRANCH AND BOUNDS; BRANCH-AND-BOUND ALGORITHMS; DUAL SOLUTIONS; EXACT COMPUTATIONS; FAST COMPUTATION; MIXED-INTEGER PROGRAMMING; STRUCTURAL INFORMATION;

ALGORITHMS; LINEAR PROGRAMMING;

INTEGER PROGRAMMING;

EID: 84877983405     PISSN: 10919856     EISSN: 15265528     Source Type: Journal    
DOI: 10.1287/ijoc.1120.0501     Document Type: Article

References (24)

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