Osmolovskii N P, Veliov V M
Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland.
Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria.
Appl Math Optim. 2023;87(3):43. doi: 10.1007/s00245-022-09959-9. Epub 2023 Mar 13.
This paper presents sufficient conditions for strong metric subregularity (SMsR) of the optimality mapping associated with the local Pontryagin maximum principle for Mayer-type optimal control problems with pointwise control constraints given by a finite number of inequalities . It is assumed that all data are twice smooth, and that at each feasible point the gradients of the active constraints are linearly independent. The main result is that the second-order sufficient optimality condition for a weak local minimum is also sufficient for a version of the SMSR property, which involves two norms in the control space in order to deal with the so-called two-norm-discrepancy.
本文给出了与具有由有限个不等式给出的逐点控制约束的 Mayer 型最优控制问题的局部庞特里亚金极大值原理相关的最优性映射的强度量次正则性（SMsR）的充分条件。假设所有数据都是二次光滑的，并且在每个可行点处，有效约束的梯度是线性无关的。主要结果是，弱局部极小值的二阶充分最优性条件对于 SMSR 性质的一个版本也是充分的，该版本在控制空间中涉及两个范数以处理所谓的双范数差异。
