A compact variant of the QCR method for quadratically constrained quadratic 0-1 programs

Optimization Letters

Volumn 8, Issue 4, 2014, Pages 1213-1224

  Galli, Laura ^a   Letchford, Adam N ^b  

^a UNIVERSITY OF PISA   (Italy)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Combinatorial optimization; Quadratically constrained quadratic programming; Semidefinite programming

Indexed keywords

QUADRATIC PROGRAMMING;

COMPUTATIONAL RESULTS; CONTINUOUS RELAXATION; CONTINUOUS VARIABLES; QUADRATIC NUMBER; QUADRATICALLY CONSTRAINED QUADRATIC PROGRAMMING; SEMI-DEFINITE PROGRAMMING;

COMBINATORIAL OPTIMIZATION;

EID: 84897426032     PISSN: 18624472     EISSN: 18624480     Source Type: Journal    
DOI: 10.1007/s11590-013-0676-8     Document Type: Article

References (20)

1. Anstreicher, K. M., Fampa, M., Lee, J., Williams, J.: Using continuous nonlinear relaxations to solve constrained maximum-entropy sampling problems. Math. Program. 85, 221-240 (1999).
2. Bai, L., Mitchell, J. E., Pang, J.-S.: Using quadratic convex reformulation to tighten the convex relaxation of a quadratic program with complementarity constraints. Optim. Lett. (Published online) (2013). doi: 10. 1007/s11590-013-0647-0.
3. Billionnet, A., Elloumi, S.: Using a mixed-integer quadratic programming solver for the unconstrained quadratic 0-1 Problem. Math. Program. 109, 55-68 (2007).
4. Billionnet, A., Elloumi, S., Lambert, A.: Extending the QCR method to general mixed-integer programs. Math. Program. 131, 381-401 (2012).
5. Billionnet, A., Elloumi, S., Lambert, A.: Convex reformulations of integer quadratically constrained problems. Talk presented at the International Symposium on Mathematical Programming (ISMP), August (2012).
6. Billionnet, A., Elloumi, S., Plateau, M.-C.: Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: the QCR method. Discr. Appl. Math. 157, 1185-1197 (2009).
7. Borchers, B.: CSDP, a C library for semidefinite programming. Optim. Meth. Soft. 11, 613-623 (1999).
8. Burer, S., Saxena, A.: The MILP road to MIQCP. In: Lee, J., Leyffer, S. (eds.) Mixed-Integer Nonlinear Programming. IMA Volumes in Mathematics and its Applications, vol. 154, pp. 373-406. Springer, Berlin (2011).
9. Faye, A., Roupin, F.: Partial Lagrangian relaxation for general quadratic programming. 4OR 5, 75-88 (2007).
10. Fujie, T., Kojima, M.: Semidefinite programming relaxation for nonconvex quadratic programs. J. Glob. Opt. 10, 367-380 (1997).
11. Hammer, P. L., Rubin, A. A.: Some remarks on quadratic programming with 01 variables. RAIRO 3, 67-79 (1970).
12. Helmberg, C., Rendl, F.: Solving quadratic (0, 1)-problems by semidefinite programs and cutting planes. Math. Program. 82, 291-315 (1998).
13. Körner, F.: On duality for Boolean programming. Eur. J. Oper. Res. 46, 399-403 (1990).
14. Lemaréchal, C., Oustry, F.: SDP relaxations in combinatorial optimization from a Lagrangian viewpoint. In: Hadjisawas, N., Pardalos, P. M. (eds.) Advances in Convex Analysis and Global Optimization. Kluwer, Dortrecht (2001).
15. Lovász, L., Schrijver, A. J.: Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optim. 1, 166-190.
16. Poljak, S., Rendl, F., Wolkowicz, H.: A recipe for semidefinite relaxation for (0, 1)-quadratic programming. J. Global Opt. 7(51-73), 1991 (1995).
17. Ramana, M.: An Algorithmic Analysis of Multiquadratic and Semidefinite Programming Problems. PhD thesis, Johns Hopkins University, Baltimore (1993).
18. Roupin, F.: From linear to semidefinite programming: an algorithm to obtain semidefinite relaxations for bivalent quadratic problems. J. Comb. Opt. 8, 469-493 (2004).
19. Sherali, H. D., Adams, W. P.: A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Kluwer, Dordrecht (1998).
20. Shor, N.: Quadratic optimization problems. Sov. J. Comput. Syst. Sci. 25, 111 (1987).