Abstract
Most existing methods of quadratically constrained quadratic optimization actually solve a refined linear or convex relaxation of the original problem. It turned out, however, that such an approach may sometimes provide an infeasible solution which cannot be accepted as an approximate optimal solution in any reasonable sense. To overcome these limitations a new approach is proposed that guarantees a more appropriate approximate optimal solution which is also stable under small perturbations of the constraints.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Al-Khayyal F.A., Larsen C., van Voorhis T. (1995): A relaxation method for nonconvex quadraticaly constrained quadratic programs. J. Glob. Optim. 6, 215–230
Audet C., Hansen P., Jaumard B., Savard G. (2000): A branch and cut algorithm for nonconvex quadratically constrained quadratic programming. Math. Program. Ser. A 87, 131–152
Dembo R.S. (1976): A set of geometric programming test problems and their solutions. Math. Program. 10, 192–213
Floudas C.A. (1999): Deterministic Global Optimization. Kluwer, Dordrecht
Floudas C.A. et al. (1999): Handbook of Test Problems in Local and Global Optimization. Kluwer, Dordrecht
Horst R., Tuy H. (1996): Global Optimization: Deterministic Approaches, 3rd edn. Springer, Berlin
Lasserre J. (2001): Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11, 796–817
Phong T.Q., Tao P.D., Hoai An L.T. (1995): A method for solving d.c. programming problems. application to fuel mixture nonconvex optimization problem. J. Glob. Optim. 6, 87–105
Sherali H.D., Tuncbilek C.H. (1992): A global opimization algorithm for polynomial programming using a reformulation-linearization technique. J. Glob. Optim. 2, 101–112
Sherali H.D., Tuncbilek C.H. (1995): A reformulation-convexification approach for solving nonconvex quadratic programming problems. J. Glob. Optim. 7, 1–31
Shor N.Z., Stetsenko S.I. (1989): Quadratic Extremal Problems and Nondifferentiable Optimization. Naukova Dumka, Kiev in Russian
Shor N.Z. (1998): Nondifferentiable Optimization and Polynomial Problems. Kluwer, Dordrecht
Tuy H. (1998): Convex Analysis and Global Optimization. Kluwer, Dordrecht
Tuy H. (2000): Monotonic optimization: problems and solution approaches. SIAM J. Optim. 11(2): 464–494
Tuy H., Al-Khayyal F., Thach P.T. (2005): Monotonic optimization: branch and cut methods. In: Audet C., Hansen P., Savard G. (eds). Essays and Surveys on Global Optimization. Springer, Berlin, pp. 39–78
Tuy H. (2005): Robust solution of nonconvex global optimization problems. J. Glob. Optim. 32, 307–323
Tuy H. (2005): Polynomial optimization: a robust approach. Pac. J. Optim. 1, 357–374
Tuy H., Minoux M., Hoai-Phuong N.T. (2006): Discrete monotonic optimization with application to a discrete location problem. SIAM J. Optim. 17, 78–97
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tuy, H., Hoai-Phuong, N.T. A robust algorithm for quadratic optimization under quadratic constraints. J Glob Optim 37, 557–569 (2007). https://doi.org/10.1007/s10898-006-9063-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9063-7