A note on representations of linear inequalities in non-convex mixed-integer quadratic programs
Tài liệu tham khảo
Adams, 1986, A tight linearization and an algorithm for zero–one quadratic programming problems, Mgmt. Sci., 32, 1274, 10.1287/mnsc.32.10.1274
Anstreicher, 2009, Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming, J. Global Optim., 43, 471, 10.1007/s10898-008-9372-0
Billionnet, 2009, Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: The QCR method, Discrete Appl. Math., 157, 1185, 10.1016/j.dam.2007.12.007
Boros, 2002, Pseudo-boolean optimization, Discrete Appl. Math., 123, 155, 10.1016/S0166-218X(01)00341-9
Burer, 2014, Unbounded convex sets for non-convex mixed-integer quadratic programming, Math. Program., 143, 231, 10.1007/s10107-012-0609-9
Burer, 2008, A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations, Math. Program., 113, 259, 10.1007/s10107-006-0080-6
Burer, 2008, A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations, Math. Program., 113, 259, 10.1007/s10107-006-0080-6
Caprara, 2008, Constrained 0–1 quadratic programming: Basic approaches and extensions, European J. Oper. Res., 187, 1494, 10.1016/j.ejor.2006.09.028
Caprara, 1999, Exact solution of the quadratic knapsack problem, INFORMS J. Comput., 11, 125, 10.1287/ijoc.11.2.125
Deza, 1997
Fortet, 1959, L’Algèbre de Boole et ses applications en recherche opérationnelle, Cahiers Centre Etudes Rech. Oper., 1, 5
Fujie, 1997, Semidefinite programming relaxation for nonconvex quadratic programs, J. Global Optim., 10, 367, 10.1023/A:1008282830093
Galli, 2011, Gap inequalities for non-convex mixed-integer quadratic programs, Oper. Res. Lett., 39, 297
Helmberg, 2000
Helmberg, 1998, Solving quadratic (0,1)-programs by semidefinite programs and cutting planes, Math. Program., 82, 291, 10.1007/BF01580072
Helmberg, 2000, A semidefinite programming approach to the quadratic knapsack problem, J. Comb. Optim., 4, 197, 10.1023/A:1009898604624
Kellerer, 2004
Lovász, 1991, Cones of matrices and set-functions and 0-1 optimization, SIAM J. Optim., 1, 166, 10.1137/0801013
Padberg, 1989, The Boolean quadric polytope: Some characteristics, facets and relatives, Math. Program., 45, 139, 10.1007/BF01589101
Poljak, 1995, A recipe for semidefinite relaxation for (0,1)-quadratic programming, J. Global Optim., 7, 51, 10.1007/BF01100205
Ramana, 1993
Sherali, 1990, A hierarchy of relaxations between the continuous and convex hull representations for zero–one programming problems, SIAM J. Discr. Math., 3, 411, 10.1137/0403036
Sherali, 1995, A reformulation-convexification approach for solving nonconvex quadratic programming problems, J. Global Optim., 7, 1, 10.1007/BF01100203