Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Gerd Wachsmuth

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

wachsmuth@b-tu.de

Keywords

  • Second order optimality condition
  • critical cone
  • polyhedricity
  • Legendre form
  • non-unique multiplier

Mathematics Subject Classification

49K27

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Suggested citation

G. Wachsmuth. “No-Gap Second-Order Conditions under n-Polyhedric Constraints and Finitely Many Nonlinear Constraints.” Journal of Convex Analysis 27 (2020), No. 2, 733–751. https://doi.org/10.68381/jca27037

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press LLC.