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Second-order asymptotic analysis for noncoercive convex optimization

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  • F. Lara

    (Universidad de Tarapacá)

Abstract

We use second-order asymptotic analysis to deal with the minimization problem of a noncoercive convex function in a reflexive Banach space. To that end, we first introduce the definition of a second-order asymptotic cone, and its respective function, based on previous results for the finite dimensional case. We provide necessary and sufficient conditions for the existence of solutions for noncoercive convex minimization problems. Examples for which our assumptions are easier to verify than other well-known results are also provided.

Suggested Citation

  • F. Lara, 2017. "Second-order asymptotic analysis for noncoercive convex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 469-483, December.
    • Handle: RePEc:spr:mathme:v:86:y:2017:i:3:d:10.1007_s00186-017-0605-1
    DOI: 10.1007/s00186-017-0605-1
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    References listed on IDEAS

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    1. Alfred Auslender, 1996. "Noncoercive Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 769-782, November.
    2. S. Deng, 2010. "Boundedness and Nonemptiness of the Efficient Solution Sets in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 29-42, January.
    3. F. Flores-Bazán & N. Hadjisavvas & F. Lara & I. Montenegro, 2016. "First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 372-393, August.
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