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Journal of Convex Analysis 27 (2020), No. 2, 733--751
Copyright Heldermann Verlag 2020

No-Gap Second-Order Conditions under n-Polyhedric Constraints and Finitely Many Nonlinear Constraints

Gerd Wachsmuth
Brandenburgische Technische Universität Cottbus-Senftenberg, Institut für Mathematik, 03046 Cottbus, Germany

We consider an optimization problem subject to an abstract constraint and finitely many nonlinear constraints. Using the recently introduced concept of n-polyhedricity, we are able to provide second-order optimality conditions under weak regularity assumptions. In particular, we prove necessary optimality conditions of first and second order under the constraint qualification of Robinson, Zowe and Kurcyusz. Similarly, sufficient optimality conditions are stated. The gap between both conditions is as small as possible.

Keywords: Second order optimality condition, critical cone, polyhedricity, Legendre form, non-unique multiplier.

MSC: 49K27.

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