Mingling: mixed-integer rounding with bounds
type: Item
instance of: scholarly article
title: Mingling: mixed-integer rounding with bounds
zbMATH Open document ID: 1190.90104
author: Oktay Günlük
author: Alper Atamtürk
published in: Mathematical Programming. Series A. Series B
publication date: 2010-04-15T00:00:00Z
review text: Mixed-integer rounding (MIR) inequalities are effective for mixed-integer programming problems with unbounded variables. The authors describe a simple procedure, called mingling, which strengthens MIR inequalities by using the information on bounds of the variables. It is shown that facets of the mixed-integer knapsack set, previously derived by subadditive lifting techniques, can be obtained by the mingling procedure. Mingling inequalities subsume the (reverse) continuous cover inequalities of \textit{H. Marchand} and \textit{L. A. Wolsey} [Math. Program. 85, No.1(A), 15--33 (1999; Zbl 0956.90021)], and the continuous integer knapsack cover and pack inequalities of \textit{A. Atamtürk} [Math. Program. 98, No. 1-3 (B), 145--175 (2003; Zbl 1082.90073)]. In some cases, mingling inequalities generalise also the two step MIR inequalities of \textit{S. Dash} and \textit{O. Günlük} [Math. Program. 105, No. 1(A), 29--53 (2006; Zbl 1085.90034)]. Mingling inequalities can easily be implemented using MIR routines. They appear to be particularly powerful after aggregating the constraints of a mixed-integer programming problem.
reviewed by: Rainer E. Burkard
Mathematics Subject Classification ID: 90C11
zbMATH DE Number: 5693205
zbMATH Keywords: mixed-integer rounding
zbMATH Keywords: cutting planes
zbMATH Keywords: subadditive lifting
MaRDI profile type: Publication
full work available at URL: s10107-009-0265-x
OpenAlex ID: W2139797076
cites work: On the facets of the mixed-integer knapsack polyhedron
cites work: Sequence Independent Lifting for Mixed-Integer Programming
cites work: Cover and pack inequalities for (mixed) integer programming
cites work: Disjunctive Programming
cites work: Edmonds polytopes and a hierarchy of combinatorial problems
cites work: Chvátal closures for mixed integer programming problems
cites work: Valid inequalities based on simple mixed-integer sets
cites work: Integer Programming and Pricing
cites work: The 0-1 knapsack problem with a single continuous variable
cites work: Aggregation and Mixed Integer Rounding to Solve MIPs
cites work: Q4040221
cites work: A recursive procedure to generate all cuts for 0-1 mixed integer programs
DOI: 10.1007/S10107-009-0265-X
description: scientific article; zbMATH DE number 5693205