No-Gap Second-Order Conditions via a Directional Curvature Functional
Optimization and Control
2021-01-26 v2
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.
Cite
@article{arxiv.1707.07579,
title = {No-Gap Second-Order Conditions via a Directional Curvature Functional},
author = {Constantin Christof and Gerd Wachsmuth},
journal= {arXiv preprint arXiv:1707.07579},
year = {2021}
}
Comments
Assumption 6.2: "$\Omega$ is bounded" was missing