Inexact Newton-Type Optimization with Iterated Sensitivities
提出一种基于迭代灵敏度的不精确牛顿型优化方法，适用于含非线性等式约束的非线性规划问题，能保持局部收敛性和渐近收缩率，并给出无伴随变体以简化实现。
This paper presents and analyzes an inexact Newton-type optimization method based on iterated sensitivities (INIS). A particular class of nonlinear programming (NLP) problems is considered, where a subset of the variables is defined by nonlinear equality constraints. The proposed algorithm considers any problem-specific approximation for the Jacobian of these constraints. Unlike other inexact Newton methods, the INIS-type optimization algorithm is shown to preserve the local convergence properties and the asymptotic contraction rate of the Newton-type scheme for the feasibility problem yielded by the same Jacobian approximation. The INIS approach results in a computational cost which can be made close to that of the standard inexact Newton implementation. In addition, an adjoint-free (AF-INIS) variant of the approach is presented which, under certain conditions, becomes considerably easier to implement than the adjoint based scheme. The applicability of these results is motivated specifically for dynamic optimization problems. In addition, the numerical performance of a corresponding open-source implementation is illustrated.