Criticality of Lagrange multipliers in extended nonlinear optimization
Criticality of Lagrange multipliers in extended nonlinear optimization
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DOI：
10.1080/02331934.2020.1723585
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发表时间：
2019-01
期刊：
影响因子：
2.2
通讯作者：
Hong-Mun Do;B. Mordukhovich;M. Sarabi
中科院分区：
文献类型：
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作者：
Hong-Mun Do;B. Mordukhovich;M. Sarabi
本文研究变分系统中拉格朗日乘子的临界性及其应用，这类问题与复合优化中的扩展非线性规划（ENLP）问题有关。在优化和变分分析的理论和数值方面，已经认识到ENLP和乘数临界性概念在变分系统中的重要性，而临界性概念从未在ENLP框架中进行过研究。我们在这里提出了一个系统的研究在一般变分设置的关键和非关键乘数，特别是覆盖了在ENLP的KKT系统，建立他们的可验证的特征，以及非临界和其他稳定性概念之间的关系，在变分分析。我们的方法主要基于二阶变分分析和广义微分的先进工具。
ABSTRACT The paper is devoted to the study and applications of criticality of Lagrange multipliers in variational systems, which are associated with the class of problems in composite optimization known as extended nonlinear programming (ENLP). The importance of both ENLP and the concept of multiplier criticality in variational systems has been recognized in theoretical and numerical aspects of optimization and variational analysis, while the criticality notion has never been investigated in the ENLP framework. We present here a systematic study of critical and noncritical multipliers in a general variational setting that covers, in particular, KKT systems in ENLP with establishing their verifiable characterizations as well as relationships between noncriticality and other stability notions in variational analysis. Our approach is mainly based on advanced tools of second-order variational analysis and generalized differentiation.