The paper provides second-order sufficient conditions for the strong local optimality of bang–bang–singular extremals in a Mayer problem with general end point constraints. The sufficient conditions are expressed as a strengthening of the necessary ones plus the coerciveness of a suitable quadratic form related to a sub-problem of the given one. The sufficiency of the given conditions is proven via Hamiltonian methods.

中文翻译：

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Bang-Bang-Singular 极值的强局部最优性：一般约束

该论文为具有一般端点约束的 Mayer 问题中 bang-bang-singular 极值的强局部最优性提供了二阶充分条件。充分条件表示为必要条件的加强加上与给定问题的子问题相关的合适的二次形式的强制性。通过哈密顿方法证明给定条件的充分性。