Quadratic knapsack problems

1980 ◽  
pp. 132-149 ◽  
Author(s):  
G. Gallo ◽  
P. L. Hammer ◽  
B. Simeone
Keyword(s):  
Knapsack Problems ◽  
Quadratic Knapsack

On reduction of duality gap in quadratic knapsack problems

2012 ◽  
Vol 54 (2) ◽  
pp. 325-339 ◽  
Author(s):  
X. J. Zheng ◽  
X. L. Sun ◽  
D. Li ◽  
Y. F. Xu
Keyword(s):  
Duality Gap ◽  
Knapsack Problems ◽  
Quadratic Knapsack

AN IMPROVED CONVEX 0-1 QUADRATIC PROGRAM REFORMULATION FOR CHANCE-CONSTRAINED QUADRATIC KNAPSACK PROBLEMS

2013 ◽  
Vol 30 (03) ◽  
pp. 1340009 ◽  
Author(s):  
SHUHUI JI ◽  
XIAOJIN ZHENG ◽  
XIAOLING SUN
Keyword(s):  
Matrix Decomposition ◽  
Knapsack Problems ◽  
Quadratic Program ◽  
Optimal Parameters ◽  
Piecewise Linearization ◽  
General Matrix ◽  
Random Size ◽  
Comparison Results ◽  
Continuous Relaxation ◽  
Quadratic Knapsack

We consider a chance-constrained quadratic knapsack problem (CQKP) where each item has a random size that is finitely distributed. We present a new convex 0-1 quadratic program reformulation for CQKP. This new reformulation improves the existing reformulation for general 0-1 quadratic program based on diagonal perturbation in the sense that the continuous relaxation of the new reformulation is tighter than or at least as tight as that of the existing reformulation. The improved reformulation is derived from a general matrix decomposition of the objective function and piecewise linearization of 0-1 variables. We show that the optimal parameters in the improved reformulation can be obtained by solving an SDP problem. Extension to k-item probabilistic quadratic knapsack problems is also discussed. Preliminary comparison results are reported to demonstrate the effectiveness of the improved reformulation.

Improving an exact approach for solving separable integer quadratic knapsack problems

2010 ◽  
Vol 23 (1) ◽  
pp. 21-28
Author(s):  
Federico Della Croce ◽  
Dominique Quadri
Keyword(s):  
Knapsack Problems ◽  
Exact Approach ◽  
Quadratic Knapsack

Dual mean field search for large scale linear and quadratic knapsack problems

2017 ◽  
Vol 478 ◽  
pp. 158-167 ◽  
Author(s):  
Juan Banda ◽  
Jonás Velasco ◽  
Arturo Berrones
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Knapsack Problems ◽  
Quadratic Knapsack

Local minima for indefinite quadratic knapsack problems

1992 ◽  
Vol 54 (1-3) ◽  
pp. 127-153 ◽  
Author(s):  
Stephen A. Vavasis
Keyword(s):  
Knapsack Problems ◽  
Local Minima ◽  
Indefinite Quadratic ◽  
Quadratic Knapsack

Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction

2007 ◽  
Vol 19 (2) ◽  
pp. 280-290 ◽  
Author(s):  
W. David Pisinger ◽  
Anders Bo Rasmussen ◽  
Rune Sandvik
Keyword(s):  
Knapsack Problems ◽  
Quadratic Knapsack
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