Parabolic regularity in geometric variational analysis
Parabolic regularity in geometric variational analysis
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DOI：
10.1090/tran/8253
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发表时间：
2019-08
影响因子：
1.3
通讯作者：
Ashkan Mohammadi;B. Mordukhovich;M. Sarabi
中科院分区：
文献类型：
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作者：
Ashkan Mohammadi;B. Mordukhovich;M. Sarabi
本文主要致力于系统的发展和应用的几何方面的二阶变分分析是围绕着抛物正则集的概念。这个概念在变分分析中已经存在二十多年了，但在很大程度上尚未得到充分研究。我们发现抛物正则性是变分分析中主要的二阶广义微分构造的新的微积分规则和计算公式的关键，它与经典微分几何和几何测度论中集合的某些性质有关。二阶变分分析和广义微分的既定结果，被嫁给发达的微积分的抛物正则性，使我们能够获得新的应用，以定性和定量/数值方面的约束优化，包括二阶最优性条件，增广拉格朗日等弱约束资格。
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in variational analysis for more than two decades while being largely underinvestigated. We discover here that parabolic regularity is the key to derive new calculus rules and computation formulas for major second-order generalized differential constructions of variational analysis in connection with some properties of sets that go back to classical differential geometry and geometric measure theory. The established results of second-order variational analysis and generalized differentiation, being married to the developed calculus of parabolic regularity, allow us to obtain novel applications to both qualitative and quantitative/numerical aspects of constrained optimization including second-order optimality conditions, augmented Lagrangians, etc. under weak constraint qualifications.