Abstract
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.
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Notes
Note that in the literature of sufficient second-order conditions, the term strong is usually associated with a condition, where the critical cone is replaced by the smallest subspace containing it, which is not the use we consider here.
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Acknowledgements
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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Nikolai Pavlovich Osmolovskii.
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Haeser, G., Ramos, A. New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization. J Optim Theory Appl 184, 494–506 (2020). https://doi.org/10.1007/s10957-019-01603-x
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DOI: https://doi.org/10.1007/s10957-019-01603-x