论文信息 - Sequence Independent Lifting for Mixed-Integer Programming

Sequence Independent Lifting for Mixed-Integer Programming

We show that superadditive lifting functions lead to sequence independent lifting of inequalities for general mixed-integer programming. As an application, we note that mixed-integer rounding (MIR) may be viewed as sequence independent lifting. Consequently, we obtain facet conditions for MIR inequalities for mixed-integer knapsacks.

A. Atamtūrk | Alper Atamtūrk

[1] Laurence A. Wolsey,et al. Valid Inequalities and Superadditivity for 0-1 Integer Programs , 1977, Math. Oper. Res..

[2] Laurence A. Wolsey,et al. A recursive procedure to generate all cuts for 0–1 mixed integer programs , 1990, Math. Program..

[3] Laurence A. Wolsey,et al. Aggregation and Mixed Integer Rounding to Solve MIPs , 2001, Oper. Res..

[4] Laurence A. Wolsey,et al. Integer and Combinatorial Optimization , 1988 .

[5] Laurence A. Wolsey,et al. Technical Note - Facets and Strong Valid Inequalities for Integer Programs , 1976, Oper. Res..

[6] Gérard Cornuéjols,et al. Elementary closures for integer programs , 2001, Oper. Res. Lett..

[7] William J. Cook,et al. Chvátal closures for mixed integer programming problems , 1990, Math. Program..

[8] R. Gomory. AN ALGORITHM FOR THE MIXED INTEGER PROBLEM , 1960 .

[9] Alper Atamtürk,et al. On the facets of the mixed–integer knapsack polyhedron , 2003, Math. Program..

[10] Gérard Cornuéjols,et al. K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau , 2003, INFORMS J. Comput..

[11] Martin W. P. Savelsbergh,et al. Sequence Independent Lifting in Mixed Integer Programming , 2000, J. Comb. Optim..