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Journal of Convex Analysis 17 (2010), No. 3&4, 789--804
Copyright Heldermann Verlag 2010

On Minimizing Quadratically Constrained Ratio of Two Quadratic Functions

Amir Beck
Dept. of Industrial Engineering and Management, Technion - Israel Institute of Technology, Haifa 32000, Israel

Marc Teboulle
School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel

We consider the nonconvex problem minimizing the ratio of two quadratic functions over finitely many nonconvex quadratic inequalities. Relying on the homogenization technique we establish a sufficient condition that warrants the attainment of an optimal solution. Our result allows to extend and recover known conditions for some interesting special instances of the problem and to derive further results on its algorithmic and modeling aspects.

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