基于方向曲率泛函的无间隙二阶条件
No-Gap Second-Order Conditions via a Directional Curvature Functional
摘要：
本文研究了有限维和无限维约束最优化问题解的二阶充要条件。利用一个适当定义的方向曲率泛函的容许集，我们得到了无间隙的二阶最优性条件在一个抽象的功能分析设置。我们的理论不仅涵盖了那些情况下，多面体或二阶正则性的经典假设得到满足，但也允许在没有这些要求的情况下研究问题。作为一个具体的例子，我们考虑了bang-bang最优控制问题的无间隙二阶条件。
英文摘要：
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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