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arXiv · 1707.07579

No-Gap Second-Order Conditions via a Directional Curvature Functional

Constantin Christof·Gerd Wachsmuth
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Abstract

This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible set, we derive no-gap second-order optimality conditions in an abstract functional analytic setting. Our theory not only covers those cases where the classical assumptions of polyhedricity or second-order regularity are satisfied but also allows to study problems in the absence of these requirements. As a tangible example, we consider no-gap second-order conditions for bang-bang optimal control problems.

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Constantin Christof, Gerd Wachsmuth. 2017-07-24. No-Gap Second-Order Conditions via a Directional Curvature Functional. https://doi.org/10.1137/17m1140418

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