No-Gap Second-Order Conditions via a Directional Curvature Functional
本文利用方向曲率泛函，在抽象泛函分析框架下推导了有限维和无限维约束优化问题的无间隙二阶最优性条件，覆盖了经典假设不成立的情形，并应用于bang-bang最优控制问题。
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.