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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