Modeling disjunctive constraints with a logarithmic number of binary variables and constraints

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5035 LNCS, Issue , 2008, Pages 199-213

  Vielma, Juan Pablo ^a   Nemhauser, George L ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE APPLICATIONS; CHEMICAL MODIFICATION; COMBINATORIAL MATHEMATICS; COMBINATORIAL OPTIMIZATION; DYNAMIC PROGRAMMING; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; LINEAR PROGRAMMING; MATHEMATICAL PROGRAMMING; NONLINEAR PROGRAMMING; NUMBER THEORY; OPTIMIZATION; PIECEWISE LINEAR TECHNIQUES; VARIATIONAL TECHNIQUES; VIBRATIONS (MECHANICAL);

(I ,J) CONDITIONS; (MIN ,MAX ,+) FUNCTIONS; (PL) PROPERTIES; BINARY VARIABLES; COMPUTATIONAL RESULTS; CONTINUOUS VARIABLES; DISJUNCTIVE CONSTRAINTS; HEIDELBERG (CO); INTERNATIONAL CONFERENCES; LINEAR PIECES; MIXED INTEGERS; PIECE-WISE LINEAR (PWL) FUNCTIONS; SPRINGER (CO); SUFFICIENT CONDITIONS (SC);

INTEGER PROGRAMMING;

EID: 45749150777     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-68891-4_14     Document Type: Conference Paper

References (37)

1. Jeroslow, R.G.: Representability in mixed integer programming 1: characterization results. Discrete Applied Mathematics 17, 223-243 (1987)
2. Jeroslow, R.G., Lowe, J.K.: Modeling with integer variables. Mathematical Programming Study 22, 167-184 (1984)
3. Lowe, J.K.: Modelling with Integer Variables. PhD thesis, Georgia Institute of Technology (1984)
4. Balas, E.: Disjunctive programming. Annals of Discrete Mathematics 5, 3-51 (1979)
5. Balas, E.: Disjunctive programming and a hierarchy of relaxations for discrete optimization problems. SIAM Journal on Algebraic and Discrete Methods 6, 466-486 (1985)
6. Balas, E.: Disjunctive programming: Properties of the convex hull of feasible points. Discrete Applied Mathematics 89, 3-44 (1998)
7. Blair, C.: 2 rules for deducing valid inequalities for 0-1 problems. SIAM Journal on Applied Mathematics 31, 614-617 (1976)
8. Jeroslow, R.G.: Cutting plane theory: disjunctive methods. Annals of Discrete Mathematics 1, 293-330 (1977)
9. Sherali, H.D., Shetty, C.M.: Optimization with Disjunctive Constraints. Lecture Notes in Economics and Mathematical Systems, vol. 181. Springer, Heidelberg (1980)
10. Balas, E.: On the convex-hull of the union of certain polyhedra. Operations Research Letters 7, 279-283 (1988)
11. Blair, C.: Representation for multiple right-hand sides. Mathematical Programming 49, 1-5 (1990)
12. Jeroslow, R.G.: A simplification for some disjunctive formulations. European Journal of Operational Research 36, 116-121 (1988)
13. Garfinkel, R.S., Nemhauser, G.L.: Integer Programming. John Wiley & Sons, Inc., Chichester (1972)
14. Watters, L.J.: Reduction of integer polynomial programming problems to zero-one linear programming problems. Operations Research 15, 1171-1174 (1967)
15. Ibaraki, T.: Integer programming formulation of combinatorial optimization problems. Discrete Mathematics 16, 39-52 (1976)
16. Nemhauser, G.L., Wolsey, L.A.: Integer and combinatorial optimization. Wiley-Interscience, Chichester (1988)
17. Balas, E.: Projection, lifting and extended formulation in integer and combinatorial optimization. Annals of Operations Research 140, 125-161 (2005)
18. Beale, E.M.L., Tomlin, J.A.: Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. In: Lawrence, J. (ed.) OR 69. Proceedings of the fifth international conference on operational research, pp. 447-454. Tavistock Publications (1970)
19. Dantzig, G.B.: On the significance of solving linear-programming problems with some integer variables. Econometrica 28, 30-44 (1960)
20. Markowitz, H.M., Manne, A.S.: On the solution of discrete programming-problems. Econometrica 25, 84-110 (1957)
21. de Farias Jr., I.R., Johnson, E.L., Nemhauser, G.L.: Branch-and-cut for combinatorial optimization problems without auxiliary binary variables. The Knowledge Engineering Review 16, 25-39 (2001)
22. Keha, A.B., de Farias, I.R., Nemhauser, G.L.: Models for representing piecewise linear cost functions. Operations Research Letters 32, 44-48 (2004)
23. Keha, A.B., de Farias, I.R., Nemhauser, G.L.: A branch-and-cut algorithm without binary variables for nonconvex piecewise linear optimization. Operations Research 54, 847-858 (2006)
24. Martin, A., Moller, M., Moritz, S.: Mixed integer models for the stationary case of gas network optimization. Mathematical Programming 105, 563-582 (2006)
25. Vielma, J.P., Keha, A.B., Nemhauser, G.L.: Nonconvex, lower semicontinuous piecewise linear optimization. Discrete Optimization 5, 467-488 (2008)
26. Croxton, K.L., Gendron, B., Magnanti, T.L.: A comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problems. Management Science 49, 1268-1273 (2003)
27. Magnanti, T.L., Stratila, D.: Separable concave optimization approximately equals piecewise linear optimization. In: Bienstock, D., Nemhauser, G.L. (eds.) IPCO 2004. LNCS, vol. 3064, pp. 234-243. Springer, Heidelberg (2004)
28. Padberg, M.: Approximating separable nonlinear functions via mixed zero-one programs. Operations Research Letters 27, 1-5 (2000)
29. Sherali, H.D.: On mixed-integer zero-one representations for separable lower-semicontinuous piecewise-linear functions. Operations Research Letters 28, 155-160 (2001)
30. Wilf, H.S.: Combinatorial algorithms-an update. In: CBMS-NSF regional conference series in applied mathematics. Society for Industrial and Applied Mathematics, vol. 55 (1989)
31. Appleget, J.A., Wood, R.K.: Explicit-constraint branching for solving mixed-integer programs. In: Laguna, M., González Velarde, J.L. (eds.) Computing tools for modeling, optimization, and simulation: interfaces in computer science and operations research. Operations research / computer science interfaces series, vol. 12, pp. 245-261. Kluwer Academic, Dordrecht (2000)
32. Shields, R.: Personal communication (2007)
33. Lee, J., Wilson, D.: Polyhedral methods for piecewise-linear functions I: the lambda method. Discrete Applied Mathematics 108, 269-285 (2001)
34. Tomlin, J.: A suggested extension of special ordered sets to non-separable non-convex programming problems. In: Hansen, P. (ed.) Studies on Graphs and Discrete Programming. Annals of Discrete Mathematics, vol. 11, pp. 359-370. North Holland, Amsterdam (1981)
35. Wilson, D.: Polyhedral methods for piecewise-linear functions. PhD thesis, University of Kentucky (1998)
36. Todd, M.J.: Union jack triangulations. In: Karamardian, S. (ed.) Fixed Points: algorithms and applications, pp. 315-336. Academic Press, London (1977)
37. Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1963)