Approximate formulations for 0-1 knapsack sets

Operations Research Letters

Volumn 36, Issue 3, 2008, Pages 317-320

  Bienstock, Daniel ^a  

^a Columbia University ^*  (United States)

Author keywords

Approximation algorithms; Integer programming; Lift and project

Indexed keywords

APPROXIMATION ALGORITHMS; INTEGER PROGRAMMING; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; RANDOM VARIABLES;

APPROXIMATE FORMULATIONS; INTEGER PROGRAMS; KNAPSACK SETS;

SET THEORY;

EID: 42949162034     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.orl.2007.09.003     Document Type: Article

References (14)

1. Balas E. Disjunctive Programs: Cutting Planes from Logical Conditions. In: Mangasarian O.L., et al. (Ed). Nonlinear Programming vol. 2 (1975), Academic Press 279-312
2. Balas E., Ceria S., and Cornuéjols G. A lift-and-project cutting plane algorithm for mixed 0-1 programs. Math. Program. 58 (1993) 295-324
3. Bienstock D., and Özbay N. Tree-width and the Sherali-Adams operator. Discrete Optim. 1 (2004) 13-22
4. Bienstock D., and Zuckerberg M. Subset Algebra Lift Operators for 0-1 integer programming. SIAM J. Optim. 15 (2004) 63-95
5. Bienstock D., and Zuckerberg M. Approximate fixed-rank closures of covering problems. Math. Program. 105 (2006) 9-27
6. Cook W., and Dash S. On the matrix-cut rank of polyhedra. Math. Oper. Res. 26 (2001) 19-30
7. Goemans M.X., and Tunçel L. When does the positive semidefiniteness constraint help in lifting procedures?. Math. Oper. Res. 26 (2001) 796-815
8. Ibarra O.H., and Kim C.E. Fast approximation algorithms for the knapsack and sum of subsets problems. J. ACM 22 (1975) 463-468
9. E.L. Lawler, Fast approximation schemes for knapsack problems, in: Proc. 18th. FOCS, 1977, pp. 206-213
10. Lovász L., and Schrijver A. Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optim. 1 (1991) 166-190
11. Laurent M. A Comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre relaxations for 0-1 programming. Math. Oper. Res. 28 (2003) 470-496
12. Lasserre J.B. An explicit exact SDP relaxation for nonlinear 0-1 programs. In: Aardal K., and Gerards A.M.H. (Eds). Lecture Notes in Computer Science (2001) 293-303
13. Sherali S., and Adams W. A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discrete Math. 3 (1990) 411-430
14. Van Vyve M., and Wolsey L.A. Approximate extended formulations. Math. Program. 105 (2006) 501-522