Wolsey, L. A. 1975. Faces for a linear inequality in 0-1 variables. Mathematical Programming 8, 165-178. Home/Search Document Not in Database Summary Related Articles Check |
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Computational Experience with Parallel Mixed Integer.. - Distributed (Correct)
....coefficient corresponding to a jmin is positive, we correct this cover by discarding a jmin . If that results in a feasible solution with an objective value less than 1, we again obtain a violated cover. After identifying a violated cover, it is lifted (in both forward and reverse passes) [4, 20, 21]. We approximate the lifting coefficients by solving the linear programming relaxations of the corresponding lifting problems. 2.2.3 Clique Cuts We employ the following exact procedure to find lifted 2 covers. Consider again a constraint of the form: X j2B a j x j b: where a, b, and x ....
L. A. Wolsey, "Faces for a linear inequality in 0--1 variables," Mathematical Programming 8 (1975) 165--178.
Polyhedral Techniques in Combinatorial Optimization II.. - Aardal, van Hoesel (1995) (1 citation) (Correct)
....to the knapsack problem. Let C be a subset of N such that P j2C a j b, and such that C is minimal with respect to this property, i.e. P j2S a j b for all S ae C. We call the set C a minimal cover with respect to N and b. In Part I we described the family of knapsack cover inequalities (Balas (1975), Hammer et al. 1975) and Wolsey (1975) X j2C x j jCj Gamma 1: 17) The inequalities (17) are valid for XK since, if we include all items in C in the knapsack, we exceed the right hand side b, which means that we have to exclude at least one of the elements in C. In Part I we discussed the ....
....presented in Theorems 3 and 4, we can conclude that conv(XK ) has a facet of the following form X j2NnN 0 ff j x j X j2N 0 nC 0 fi j x j X j2C 0 x j jC 0 j Gamma 1 X j2N 0 nC 0 fi j ; 18) where ff j 0 for all j 2 N n N 0 and fi j 0 for all j 2 N 0 n C 0 . Balas (1975) characterized the lifting coefficients ff j in the case where N 0 n C 0 = The family of (1; k) configuration inequalities (Padberg (1980) is defined as follows. Let C N , and t 2 N n C be such that P j2 C a j b and such that Q[ ftg is a minimal cover for all Q C with jQj ....
[Article contains additional citation context not shown here]
L.A. Wolsey (1975) "Faces for a linear inequality in 0-1 variables", Mathematical Programming 8 165--178.
Parallel Mixed Integer Programming - Bixby, Cook, Cox, Lee (1995) (4 citations) (Correct)
....coefficient corresponding to a jmin is positive, we correct this cover by discarding a jmin . If that results in a feasible solution with an objective value less than 1, we again obtain a violated cover. After identifying a violated cover, it is lifted (in both forward and reverse passes) [4, 20, 21]. We approximate the lifting coefficients by solving the linear programming relaxations of the corresponding lifting problems. 2.2.3 Clique Cuts We employ the following exact procedure to find lifted 2 covers. Consider again a constraint of the form: X j2B a j x j b: where a, b, and ....
L. A. Wolsey, "Faces for a linear inequality in 0--1 variables," Mathematical Programming 8 (1975) 165--178.
Polyhedral Techniques in Combinatorial Optimization II.. - Aardal, van Hoesel (1995) (1 citation) (Correct)
....the feasible solutions to the knapsack problem. Let C be a subset of N such that P j2C a j b, and such that C is minimal with respect to this property, i.e. P j2S a j b for all S ae C. We call the set C a minimal cover. In Part I we described the family of knapsack cover inequalities (Balas (1975), Hammer et al. 1975) and Wolsey (1975) X j2C x j jCj Gamma 1: 14) The inequalities (14) are valid for XK since, if we include all items in C in the knapsack, we exceed the right hand side b, which means that we have to exclude at least one of the elements in C. In Part I we discussed the ....
....presented in Theorems 3 and 4, we can conclude that conv(XK ) has a facet of the following form X j2NnN 0 ff j x j X j2N 0 nC 0 fi j x j X j2C 0 x j jC 0 j Gamma 1 X j2N 0 nC 0 fi j ; 15) where ff j 0 for all j 2 N n N 0 and fi j 0 for all j 2 N 0 n C 0 . Balas (1975) characterized the lifting coefficients ff j in the case where N 0 n C 0 = The family of (1; k) configuration inequalities (Padberg (1980) is defined as follows. Let C N , and t 2 N n C be such that P j2 C a j b and such that Q[ ftg is a minimal cover for all Q C with ....
[Article contains additional citation context not shown here]
L.A. Wolsey (1975) "Faces for a linear inequality in 0-1 variables", Mathematical Programming 8 165--178.
Polyhedral Techniques in Combinatorial Optimization I: Theory - Aardal, van Hoesel (1995) (1 citation) (Correct)
....We call a set C a cover, or a dependent set, with respect to N if P j2C a j b. A cover is minimal if P j2S a j b for all S ae C. If we choose all elements from the cover C, it is clear that the righthand side of (17) is exceeded. Hence, the following knapsack cover inequality (Balas (1975), Hammer et al. 1975) and Wolsey (1975) X j2C x j jCj Gamma 1 (19) is valid. A generalization of (19) is given by the family of (1; k) configuration inequalities (Padberg (1980) Let C N , and t 2 N n C be such that P j2 C a j b and such that Q [ ftg is a minimal cover for ....
L.A. Wolsey (1975) "Faces for a linear inequality in 0-1 variables", Mathematical Programming 8 165--178.
Implementing the Dantzig-Fulkerson-Johnson Algorithm.. - Applegate, Bixby.. (2003) (2 citations) (Correct)
No context found.
Wolsey, L. A. 1975. Faces for a linear inequality in 0-1 variables. Mathematical Programming 8, 165-178.
Capacitated Facility Location: Separation Algorithms and.. - Aardal (1994) (6 citations) (Correct)
No context found.
L.A. Wolsey (1975). "Faces for a linear inequality in 0-1 variables". Mathematical Programming 8 165--178.
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