Abstract
We consider the maximization of a ratio f of an arbitrary quadratic function and an affine function over a closed and unbounded set. The behavior of unbounded feasible sequences is studied in order to derive a) conditions under which f attains a finite supremum and b) conditions which guarantee that its supremum is finite. We first consider a function f where the quadratic form is semidefinite. We then obtain results for the case where the quadratic function is the product of two affine functions.
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© 2001 Springer-Verlag Berlin Heidelberg
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Cambini, A., Carosi, L., Martein, L. (2001). On the Supremum in Quadratic Fractional Programming. In: Hadjisavvas, N., Martínez-Legaz, J.E., Penot, JP. (eds) Generalized Convexity and Generalized Monotonicity. Lecture Notes in Economics and Mathematical Systems, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56645-5_8
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DOI: https://doi.org/10.1007/978-3-642-56645-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41806-1
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