Geodesic
On Minimizing Quadratically Constrained Ratio of Two Quadratic Functions
Journal of convex analysis, Tome 17 (2010) no. 3, pp. 789-804.

Voir la notice de l'article provenant de la source Heldermann Verlag

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. 
@article{JCA_2010_17_3_JCA_2010_17_3_a6,
     author = {A. Beck and M. Teboulle},
     title = {On {Minimizing} {Quadratically} {Constrained} {Ratio} of {Two} {Quadratic} {Functions}},
     journal = {Journal of convex analysis},
     pages = {789--804},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a6/}
}
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A. Beck; M. Teboulle. On Minimizing Quadratically Constrained Ratio of Two Quadratic Functions. Journal of convex analysis, Tome 17 (2010) no. 3, pp. 789-804. http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a6/