New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization

  • G. HaeserEmail author
  • A. Ramos


In this paper, we present and discuss new constraint qualifications to ensure the validity of well-known second-order properties in nonlinear optimization. Here, we discuss conditions related to the so-called basic second-order condition, where a new notion of polar pairing is introduced in order to replace the polar operation, useful in the first-order case. We then proceed to define our second-order constraint qualifications, where we present an approach similar to the Guignard constraint qualification in the first-order case.


Nonlinear optimization Constraint qualifications Second-order optimality conditions 

Mathematics Subject Classification

90C30 90C46 



The first author was supported by FAPESP (Grants 2013/05475-7, 2017/18308-2 and 2018/24293-0) and CNPq. The second author was funded by CNPq, Grants 454798/2015-6 and 438185/2018-8.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of São PauloSão PauloBrazil
  2. 2.Department of MathematicsFederal University of ParanáCuritibaBrazil

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