Journal of Convex Analysis 25 (2018), No. 1, 271--291
Copyright Heldermann Verlag 2018
Second Order Asymptotic Functions and Applications to Quadratic Programming
Alfredo N. Iusem
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, CEP 22460-320, Brazil
iusp@impa.br
Felipe Lara
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Tarapacá, Arica, Chile
felipelaraobreque@gmail.com
We introduce a new second order asymptotic function which gives information on the convexity (concavity) of the original function from its behavior at infinity. We establish several properties and calculus rules for this concept, which differs from previous notions of second order asymptotic function. Finally, we apply our new definition in order to obtain necessary and sufficient optimality conditions for quadratic programming and quadratic fractional programming.
Keywords: Asymptotic cone, asymptotic function, second order asymptotic functions, generalized convexity, quadratic programming, quadratic fractional programming.
MSC: 90C20, 90C26, 90C32
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