Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Alfredo N. Iusem

Instituto de Matemática Pura e Aplicada, Estrada Doña Castorina 110, Jardim Botânico, Rio de Janeiro, CEP 22460-320, Brazil

iusp@impa.br

Keywords

  • Asymptotic cone
  • asymptotic function
  • second order asymptotic functions
  • generalized convexity
  • quadratic programming
  • quadratic fractional programming

Mathematics Subject Classification

90C20, 90C26, 90C32

Suggested citation

A. N. Iusem, F. Lara. “Second Order Asymptotic Functions and Applications to Quadratic Programming.” Journal of Convex Analysis 25 (2018), No. 1, 271–291. https://doi.org/10.68381/jca25016

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.