Convex relaxation and Lagrangian decomposition for indefinite integer quadratic programming

Optimization

Volumn 59, Issue 5, 2010, Pages 627-641

  Sun, X L ^a   Li, J L ^b   Luo, H Z ^c  

^a FUDAN UNIVERSITY   (China)

^b GUANGXI UNIVERSITY   (China)

^c ZHEJIANG UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Branch and bound method; Convex relaxation; Indefinite integer quadratic programming; Lagrangian decomposition; Lower bounds

Indexed keywords

EID: 77953832368     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331930801987607     Document Type: Article

References (30)

1. C.S. Adjiman, I.P. Androulakis, and C.A. Floudas, A global optimization method, aBB, for general twice-differentiable constrained NLPs - II. Implementation and computational results, Comp. Chem. Eng. 22 (1998), pp. 1159-1179.
2. C.S. Adjiman et al., A global optimization method, aBB, for general twice-differentiable constrained NLPs -I. Theoretical advances, Comp. Chem. Eng. 22 (1998), pp. 1137-1158.
3. L.T.H An and P.D. Tao, Solving a class of linearly constrained indefinite quadratic problems by D.C. algorithms, J. Global Optim. 11 (1997), pp. 253-285.
4. L.T.H An and P.D. Tao, A branch and bound method via D. C. optimization algorithms and ellipsoidal technique for box constrained nonconvex quadratic problems, J. Global. Optim. 13 (1998), pp. 171-206.
5. L.T.H An, P.D. Tao, and L.D. Muu, A combined dc optimization-ellipsoidal branch-and-bound algorithm for solving nonconvex quadratic programming problems, J. Comb. Optim. 2 (1998), pp. 9-28.
6. O. Barrientos and R. Correa, An algorithm for global minimization of linearly constrained quadratic functions, J. Global. Optim. 16 (2000), pp. 77-93.
7. M.W. Carter, The indefinite zero-one quadratic problem, Dis Appl Math 7 (1984), pp. 23-44.
8. S.S. Erenguc and H.P. Benson, An algorithm for indefinite integer quadratic programming, Com. Math. Appl. 21 (1991), pp. 99-106.
9. C.A. Floudas, Deterministic Global Optimization: Theory and Applications, Kluwer Academic Publishers, Dordrecht, 2000.
10. C.A. Floudas and V. Visweswaran, A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory, Comp. Chem. Eng. 14 (1990), pp. 1397-1417.
11. C.A. Floudas and V. Visweswaran, A primal-relaxed dual global optimization approach, J. Optim. Theory Appl. 78 (1993), pp. 187-225.
12. C.A. Floudas and V. Visweswaran, Quadratic optimization in Handbook of Global Optimization, R. Horst and P.M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, 1995, pp. 217-269.
13. P.E. Gill and W. Murray, Numerically stable methods for quadratic programming, Math. Program. 14 (1978), pp. 349-372.
14. P. Hansen, B. Jaumard, and V. Mathon, Constrained nonlinear 0-1 programming, ORSA. J. Comp. 5 (1993), pp. 97-119.
15. N.J. Jobst et al., Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints, Quant. Finance 1 (2001), pp. 489-501.
16. P.F. Kough, The indefinite quadratic programming problem, Oper. Res. 27 (1979), pp. 516-533.
17. D. Li and X.L. Sun, Nonlinear Integer Programming, Springer, New York, 2006.
18. D. Li, X.L. Sun, and F.L. Wang, Convergent Lagrangian and contour-cut method for nonlinear integer programming with a quadratic objective function, SIAM J. Optim. 17 (2006), pp. 372-400.
19. D. Li, X.L. Sun, and F.L. Wang, Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection, Math. Finance 16 (2006), pp. 83-101.
20. R.D. Mcbride and J.S. Yormark, An implicit enumeration algorithm for quadratic integer programming, Manage. Sci. 26 (1980), pp. 282-296.
21. P.M. Pardalos, J.H. Glick, and J.B. Rosen, Global minimization of indefinite quadratic problems, Computing 39 (1987), pp. 281-291.
22. P.M. Pardalos and J.B. Rosen, Constrained Global Optimization: Algorithms and Applications, Springer-Verlag, Berlin, 1987.
23. A.T. Phillips and J.B. Rosen, Guaranteed -approximate solution for indefinite quadratic global minimization, Naval. Res. Logist. 37 (1990), pp. 499-514.
24. S.S. Syam, A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals, Euro. J. Oper. Res. 108 (1998), pp. 196-207.
25. N.V. Thoai, Global optimization techniques for solving the general quadratic integer programming problem, Comput. Optim. Appl. 10 (1998), pp. 149-163.
26. V. Visweswaran and C.A. Floudas, A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: II. Applications of theory and test problems, Comp. Chem. Eng. 14 (1990), pp. 1417-1434.
27. V. Visweswaran and C.A. Floudas, New properties and computational improvement of the GOP algorithm for problems with quadratic objective function and constraints, J. Global Optim. 3 (1993), pp. 439-462.
28. D. Vanderbussche and G.L. Nemhauser, A branch-and-cut algorithm for nonconvex quadratic programs with box constraints, Math. Program. 102 (2005), pp. 371-405.
29. D. Vanderbussche and G.L. Nemhauser, A polyhedral study of nonconvex quadratic programs with box constraints, Math. Program. 102 (2005), pp. 531-575.
30. Y. Yajima and T. Fujie, A polyhedral approach for nonconvex quadratic programming problems with box constraints, J. Global Optim. 13 (1998), pp. 151-170.