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Extended canonical duality and conic programming for solving 0-1 quadratic programming problems
1. | Department of Mathematical Sciences, Tsinghua University, Beijing, China |
2. | Department of Industrial and System Engineering, North Carolina State University, Raleigh, NC 27695, United States |
References:
[1] |
K. Allemand, K. Fukuda, T. M. Liebling and E. Steiner, A polynomial case of unconstrained zero-one quadratic optimization,, Mathematical Programming, 91 (2001), 49.
|
[2] |
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs,, Mathematical Programming, 120 (2009), 479.
doi: 10.1007/s10107-008-0223-z. |
[3] |
S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu, Canonical dual approach to solving 0-1 quadratic programming problem,, J. Industrial and Management Optimization, 3 (2007), 125.
|
[4] |
S.-C. Fang, D. Y. Gao, R.-L. Sheu and W. Xing, Global optimization for a class of fractional programming problems,, J. Global Optimization, 45 (2009), 337.
doi: 10.1007/s10898-008-9378-7. |
[5] |
D. Y. Gao, Canonical dual transformation method and generalized triality theory in nonsmooth global optimization,, J. Global Optimization, 17 (2000), 127.
doi: 10.1023/A:1026537630859. |
[6] |
D. Y. Gao, Advances in canonical duality theory with applications to global optimization,, available at: , (). Google Scholar |
[7] |
M. R. Garey and D. S. Johnson, "Computers and Intractability: A Guide to the Theory of NP-Completeness,", W. H. Freeman, (1979).
|
[8] |
M. X. Goemans and D. P. Williamson, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming,, J. ACM, 42 (1995), 1115.
doi: 10.1145/227683.227684. |
[9] |
V. Jeyakumar, A. M. Rubinov and Z. Y. Wu, Non-convex quadratic minimization problems with quadratic constraints: Global optimality conditions,, Mathematical Programming, 110 (2007), 521.
doi: 10.1007/s10107-006-0012-5. |
[10] |
Q. Jin, S.-C. Fang and W. Xing, On the global optimality of generalized trust region subproblems,, Optimization., ().
doi: DOI:10.1080/02331930902995236. |
[11] |
E. Klerk and D. V. Pasechnik, Approximation of the stability number of a graph via copositive programming,, SIAM J. Optimization, 12 (2002), 875.
doi: 10.1137/S1052623401383248. |
[12] |
C. Lu, Z. Wang and W. Xing, An improved lower bound and approximation algorithm for binary constrained quadratic programming problem,, J. Global Optimization., ().
doi: DOI: 10.1007/s10898-009-9504-1. |
[13] |
A. Ben-Israel and T. N. E. Greville, "Generalized Inverses,", Springer-Verlag, (2003).
|
[14] |
P. M. Pardalos and G. P. Rodgers, Computational aspects of a branch and bound algorithm for quadratic zero-one programming,, Computing, 45 (1990), 131.
doi: 10.1007/BF02247879. |
[15] |
J. F. Sturm and S. Z. Zhang, On cones of nonnegative quadratic functions,, Mathematics of Operations Research, 28 (2003), 246.
doi: 10.1287/moor.28.2.246.14485. |
[16] |
X. Sun, C. Liu, D. Li and J. Gao, On duality gap in binary quadratic programming,, aviable at: , (). Google Scholar |
[17] |
Z. Wang, S.-C. Fang, D. Y. Gao and W. Xing, Global extremal conditions for multi-integer quadratic programming,, J. Industrial and Management Optimization, 4 (2008), 213.
|
[18] |
Z. Wang, S.-C. Fang, D. Y. Gao and W. Xing, Canonical dual approach to solving the maximum cut problem,, Working Paper, (). Google Scholar |
[19] |
L. A. Wolsey, "Integer Programming,", Wiley-Interscience, (1998).
|
[20] |
W. Xing, S.-C. Fang, D. Y. Gao and L. Zhang, Canonical duality solutions to quadratic programming over a quadratic constraint,, Proceedings of ICOTA7, (2007), 35. Google Scholar |
show all references
References:
[1] |
K. Allemand, K. Fukuda, T. M. Liebling and E. Steiner, A polynomial case of unconstrained zero-one quadratic optimization,, Mathematical Programming, 91 (2001), 49.
|
[2] |
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs,, Mathematical Programming, 120 (2009), 479.
doi: 10.1007/s10107-008-0223-z. |
[3] |
S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu, Canonical dual approach to solving 0-1 quadratic programming problem,, J. Industrial and Management Optimization, 3 (2007), 125.
|
[4] |
S.-C. Fang, D. Y. Gao, R.-L. Sheu and W. Xing, Global optimization for a class of fractional programming problems,, J. Global Optimization, 45 (2009), 337.
doi: 10.1007/s10898-008-9378-7. |
[5] |
D. Y. Gao, Canonical dual transformation method and generalized triality theory in nonsmooth global optimization,, J. Global Optimization, 17 (2000), 127.
doi: 10.1023/A:1026537630859. |
[6] |
D. Y. Gao, Advances in canonical duality theory with applications to global optimization,, available at: , (). Google Scholar |
[7] |
M. R. Garey and D. S. Johnson, "Computers and Intractability: A Guide to the Theory of NP-Completeness,", W. H. Freeman, (1979).
|
[8] |
M. X. Goemans and D. P. Williamson, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming,, J. ACM, 42 (1995), 1115.
doi: 10.1145/227683.227684. |
[9] |
V. Jeyakumar, A. M. Rubinov and Z. Y. Wu, Non-convex quadratic minimization problems with quadratic constraints: Global optimality conditions,, Mathematical Programming, 110 (2007), 521.
doi: 10.1007/s10107-006-0012-5. |
[10] |
Q. Jin, S.-C. Fang and W. Xing, On the global optimality of generalized trust region subproblems,, Optimization., ().
doi: DOI:10.1080/02331930902995236. |
[11] |
E. Klerk and D. V. Pasechnik, Approximation of the stability number of a graph via copositive programming,, SIAM J. Optimization, 12 (2002), 875.
doi: 10.1137/S1052623401383248. |
[12] |
C. Lu, Z. Wang and W. Xing, An improved lower bound and approximation algorithm for binary constrained quadratic programming problem,, J. Global Optimization., ().
doi: DOI: 10.1007/s10898-009-9504-1. |
[13] |
A. Ben-Israel and T. N. E. Greville, "Generalized Inverses,", Springer-Verlag, (2003).
|
[14] |
P. M. Pardalos and G. P. Rodgers, Computational aspects of a branch and bound algorithm for quadratic zero-one programming,, Computing, 45 (1990), 131.
doi: 10.1007/BF02247879. |
[15] |
J. F. Sturm and S. Z. Zhang, On cones of nonnegative quadratic functions,, Mathematics of Operations Research, 28 (2003), 246.
doi: 10.1287/moor.28.2.246.14485. |
[16] |
X. Sun, C. Liu, D. Li and J. Gao, On duality gap in binary quadratic programming,, aviable at: , (). Google Scholar |
[17] |
Z. Wang, S.-C. Fang, D. Y. Gao and W. Xing, Global extremal conditions for multi-integer quadratic programming,, J. Industrial and Management Optimization, 4 (2008), 213.
|
[18] |
Z. Wang, S.-C. Fang, D. Y. Gao and W. Xing, Canonical dual approach to solving the maximum cut problem,, Working Paper, (). Google Scholar |
[19] |
L. A. Wolsey, "Integer Programming,", Wiley-Interscience, (1998).
|
[20] |
W. Xing, S.-C. Fang, D. Y. Gao and L. Zhang, Canonical duality solutions to quadratic programming over a quadratic constraint,, Proceedings of ICOTA7, (2007), 35. Google Scholar |
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