Necessary optimality conditions for constrained optimization problems under the relaxed constraint qualifications
Izmailov | Arutuynov, | Avakov,
We derive first- and second-order necessary optimality conditions for set-constrained optimization problems under the constraint qualification-type conditions significantly wearker than Robinson's constraint qualification. Our development relies on the so-called 2-regularity concept, and unifies and extends the previous studies based on this concept. Specifically, in our setting constraints are given by an inclusion, with an arbitrary closed convex set in the right-hand side. Thus, for the second-order analysis, some curvature characterizations of this set near the reference point must be taken into account.