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Journal of Convex Analysis 26 (2019), No. 1, 015--032
Copyright Heldermann Verlag 2019

Quadratic Fractional Programming under Asymptotic Analysis

Felipe Lara
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Tarapacá, Arica, Chile

We consider the quadratic fractional programming problem, which minimizes a ratio of two functions; a quadratic (not necessarily convex) function over an a affine function on an unbounded set. As is well-known, if the quadratic function is convex or quasiconvex, then the quadratic fractional function is pseudoconvex, a particular case of the quasiconvex minimization problem. Thus, we develop optimality conditions for the general case by introducing a generalized asymptotic function to deal with quasiconvexity. We established two characterization results for the nonemptiness and compactness for the set of minimizers of any quasiconvex function. In addition, an extension for the Frank-Wolfe theorem from the quadratic to the quadratic fractional problem will be given. Finally, applications to pseudoconvex quadratic fractional programming are also provided.

Keywords: Asymptotic functions, second order asymptotic functions, nonconvex optimization, optimality conditions, quasiconvexity, Frank-Wolfe theorem, quadratic fractional programming.

MSC: 90C20, 90C26, 90C32

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