全扰动下平稳点集映射的灵敏度分析. 第二部分: Robinson 稳定性
最优化与控制
2018-11-15 v2
摘要
在本文的第一部分中，我们估计了带一个光滑函数约束的光滑参数优化问题在全扰动下平稳点集映射的 Fréchet 上导数与 Mordukhovich 上导数。由这些估计得到了该映射局部 Lipschitz 似性质的充要条件。在本部分中，我们建立了平稳点集映射 Robinson 稳定性的充分条件。这使我们得以重访并推广不定二次规划中的若干稳定性定理。同时给出了我们的结果与通过另一途径所得结果之比较。
引用
@article{arxiv.1811.05131,
title = {Sensitivity Analysis of a Stationary Point Set Map under Total Perturbations. Part 2: Robinson Stability},
author = {Duong Thi Kim Huyen and Jen-Chih Yao and Nguyen Dong Yen},
journal= {arXiv preprint arXiv:1811.05131},
year = {2018}
}
备注
This manuscript is based on the paper "Sensitivity Analysis of a Stationary Point Set Map under Total Perturbations. Part 2: Robinson Stability" which has been pubplished in Journal of Optimization Theory and Applications (DOI: 10.1007/s10957-018-1295-4). We have added the Section 6 "Appendices" to the paper. This section presents two proofs of Lemmas 5.1 and 5.2