Variational Analysis of Composite Models with Applications to Continuous Optimization
Variational Analysis of Composite Models with Applications to Continuous Optimization
复制标题
DOI：
10.1287/moor.2020.1074
复制
发表时间：
2019-05
期刊：
影响因子：
--
通讯作者：
Ashkan Mohammadi;B. Mordukhovich;M. Sarabi
中科院分区：
文献类型：
--
作者：
Ashkan Mohammadi;B. Mordukhovich;M. Sarabi
本文致力于综合模型的变分分析和优化的重要性，其中众多的理论，算法和应用问题的运筹学是很难夸大的综合研究。我们的研究的基本主题是一个系统的替代传统的度量正则性和相关的要求弱得多的度量subregulatity的，使我们显着更强大的和全新的结果，一阶和二阶变分分析和优化。通过这种方式，我们开发了扩展的微积分规则的一阶和二阶广义微分结构，同时支付主要注意力在二阶变分理论的新的和相当大的类完全sub顺从的成分。在优化中的应用包括在约束组合模型中导出增强的无间隙二阶最优性条件、完整刻画拉格朗日乘子的唯一性、参数优化中Karush-Kuhn-Tucker系统的强度量次正则性等。
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate. The underlying theme of our study is a systematical replacement of conventional metric regularity and related requirements by much weaker metric subregulatity ones that lead us to significantly stronger and completely new results of first-order and second-order variational analysis and optimization. In this way, we develop extended calculus rules for first-order and second-order generalized differential constructions while paying the main attention in second-order variational theory to the new and rather large class of fully subamenable compositions. Applications to optimization include deriving enhanced no-gap second-order optimality conditions in constrained composite models, complete characterizations of the uniqueness of Lagrange multipliers, strong metric subregularity of Karush-Kuhn-Tucker systems in parametric optimization, and so on.