Minimizing an indefinite quadratic function subject to a single indefinite quadratic constraint

Abstract

In this paper, we consider the problem of minimizing an indefinite quadratic function subject to a single indefinite quadratic constraint. A key difficulty with this problem is its nonconvexity. Using Lagrange duality, we show that under a mild assumption, this problem can be solved by solving a linearly constrained convex univariate minimization problem. Finally, the superior efficiency of the new approach compared to the known semidefinite relaxation and a known approach from the literature is demonstrated by solving several randomly generated test problems.

Keywords:

• Indefinite quadratic optimization
• global optimization
• diagonalization
• semidefinite optimization relaxation

Acknowledgements

The authors would like to thank the reviewer for his/her useful comments and suggestions. The second author thanks the financial support from University of Guilan.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by University of Guilan [grant number 10643].