增广拉格朗日乘子存在性：归约到精确罚函数与局部化原理
最优化与控制
2024-09-11 v3
摘要
本文给出关于增广拉格朗日乘子存在性的新一般性结果。我们定义与增广拉格朗日相关联的罚函数，并证明在增广函数满足某增长假设下，增广拉格朗日乘子存在当且仅当该罚函数精确。我们还提出一种称为局部化原理的研究增广拉格朗日乘子的新通用方法。局部化原理允许人们研究增广拉格朗日在初始优化问题全局最优解附近的局部行为，以证明增广拉格朗日乘子的存在性。
引用
@article{arxiv.1802.03046,
title = {Existence of augmented Lagrange multipliers: reduction to exact penalty functions and localization principle},
author = {M. V. Dolgopolik},
journal= {arXiv preprint arXiv:1802.03046},
year = {2024}
}
备注
This is a slightly edited verion of a pre-print of an article published in Mathematical Programming. The final authenticated version is available online at: https://doi.org/10.1007/s10107-017-1122-y In this version, a mistake in the proof of Theorem 4 was corrected