References
- Alizadeh , F. , Haeberly , J. P.A. and Overton , M. L. 1997 . Complementarity and nondegeneracy in semidefinite programming . Math. Program , 77 : 111 – 128 .
- Billionnet , A. and Soutif , E. 2004 . An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem . Eur. J. Oper. Res , 157 : 565 – 575 . (doi:10.1016/S0377-2217(03)00244-3)
- Billionnet , A. , Faye , A. and Soutif , E. 1999 . A new upper bound for the 0-1 quadratic knapsack problem . Eur. J. Oper. Res , 112 : 664 – 672 . (doi:10.1016/S0377-2217(97)00414-1)
- Caprara , A. , Pisinger , D. and Toth , P. 1999 . Exact solution of the quadratic knapsack problem . INFORMS J. Comput , 11 : 125 – 139 . (doi:10.1287/ijoc.11.2.125)
- Chaillou , P. , Hansen , P. and Mahieu , Y. 1986 . Best network flow bounds for the quadratic knapsack problem . Lecture Notes Math , 1403 : 226 – 235 .
- Gallo , G. and Simeone , B. 1988 . On the supermodular knapsack problems . Math. Program , 45 : 295 – 309 . (doi:10.1007/BF01589108)
- Gallo , G. , Hammer , P. L. and Simeone , B. 1980 . Quadratic knapsack problems . Math. Program. Study , 12 : 132 – 149 . (doi:10.1007/BFb0120892)
- Helmberg , C. , Rendl , F. and Weismantel , R. 1996 . “ Quadratic knapsack relaxations using cutting planes and semidefinite programming ” . In Integer Programming and Combinatorial Optimization , Edited by: Cunningham , W. H. , McCormick , S. T. and Queyranne , M. 175 – 189 . Vancouver , , Canada : Springer . Lecture Notes in Computer Science, Vol. 1084
- Helmberg , C. , Rendl , F. and Weismantel , R. 2000 . A semidefinite programming approach to the quadratic knapsack problem . J. Comb. Optim , 4 : 197 – 215 . (doi:10.1023/A:1009898604624)
- Malik , U. , Jaimoukha , I. M. , Halikias , G. D. and Gungah , S. K. 2006 . On the gap between the quadratic integer programming problem and its semidefinite relaxation . Math. Program , 107 : 505 – 515 . (doi:10.1007/s10107-005-0692-2)
- Michelon , P. and Veilleux , L. 1996 . Lagrangian methods for the 0-1 quadratic knapsack problem . Eur. J. Oper. Res , 92 : 326 – 341 . (doi:10.1016/0377-2217(94)00286-X)
- Pataki , G. and Tunçel , L. 2001 . On the generic properties of convex optimization problems in conic form . Math. Program , 89 : 449 – 457 . (doi:10.1007/PL00011408)
- Pisinger , D. 2007 . The quadratic knapsack problem – a survey . Discrete Appl. Math , 155 : 623 – 648 . (doi:10.1016/j.dam.2006.08.007)
- Shapiro , A. 1985 . Extremal problems on the set of nonnegative definite matrices . Linear Algebra Appl , 67 : 7 – 18 . (doi:10.1016/0024-3795(85)90182-X)
- Yildirim , E. A. 2003 . An interior-point perspective on sensitivity analysis in semidefinite programming . Math. Oper. Res , 28 : 649 – 676 . (doi:10.1287/moor.28.4.649.20511)
- Zheng , X. J. , Sun , X. L. , Li , D. and Xia , Y. 2010 . Duality gap estimation of linear equality constrained binary quadratic programming . Math. Oper. Res , 35 : 864 – 880 . (doi:10.1287/moor.1100.0472)
- X.J. Zheng, X.L. Sun, and D. Li, On the reduction of duality gap in quadratic knapsack problems, technical report, School of Management, Fudan University, Shanghai, China, 2011. Available at: http://my.gl.fudan.edu.cn/teacherhome/xlsun/qkp-gap.pdf