Separation and Extension of Cover Inequalities for Conic Quadratic Knapsack Constraints with Generalized Upper Bounds

Authors:
Alper Atamtürk;Laurent Flindt Muller;David Pisinger
Affiliations:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720;Department of Management Engineering, Technical University of Denmark, Produktionstorvet, DK-2800 Kgs. Lyngby, Denmark;Department of Management Engineering, Technical University of Denmark, Produktionstorvet, DK-2800 Kgs. Lyngby, Denmark
Venue:
INFORMS Journal on Computing
Year:
2013

Citing 16
Cited 0

Easily computable facets of the knapsack polytope

Mathematics of Operations Research
Valid inequalities for 0–1 knapsacks and mips with generalised upper bound constraints

Selected papers on First international colloquium on pseudo-boolean optimization and related topics
The complexity of lifted inequalities for the knapsack problem

Discrete Applied Mathematics
Solving Multiple Knapsack Problems by Cutting Planes

SIAM Journal on Optimization
Lifted Cover Inequalities for 0-1 Integer Programs: Computation

INFORMS Journal on Computing
Lifted Cover Inequalities for 0-1 Integer Programs: Complexity

INFORMS Journal on Computing
Convex Optimization

Convex Optimization
Cuts for mixed 0-1 conic programming

Mathematical Programming: Series A and B
Submodular function minimization

Mathematical Programming: Series A and B
Conic mixed-integer rounding cuts

Mathematical Programming: Series A and B
Lifting for conic mixed-integer programming

Mathematical Programming: Series A and B
Polymatroids and mean-risk minimization in discrete optimization

Operations Research Letters
The submodular knapsack polytope

Discrete Optimization
A note of the knapsack problem with special ordered sets

Operations Research Letters
Lifted cover facets of the 0-1 knapsack polytope with GUB constraints

Operations Research Letters
The complexity of cover inequality separation11This research was supported by US Army Research Office DAAH04-94-G-0017 and NSF Grant No. DMI-9700285.

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

Motivated by addressing probabilistic 0--1 programs we study the conic quadratic knapsack polytope with generalized upper bound GUB constraints. In particular, we investigate separating and extending GUB cover inequalities. We show that, unlike in the linear case, determining whether a cover can be extended with a single variable is NP-hard. We describe and compare a number of exact and heuristic separation and extension algorithms which make use of the structure of the constraints. Computational experiments are performed for comparing the proposed separation and extension algorithms. These experiments show that a judicious application of the extended GUB cover cuts can reduce the solution time of conic quadratic 0--1 programs with GUB constraints substantially.