Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems

被引：0
作者：
O. Cornejo
A. Jourani
C. Zălinescu
机构：
[1] Universidad de Talca,Departamento de Ingenieria de Sistemas, Aplicada
[2] Université de Bourgogne,Analyse Appliquée et Optimisation
[3] University Al. I. Cuza,Faculty of Mathematics
来源：
Journal of Optimization Theory and Applications | 1997年 / 95卷
关键词：
Subdifferentials; upper-Lipschitz property; conditioning; Ekeland variational principle;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study conditioning problems for convex and nonconvex functions defined on normed linear spaces. We extend the notion of upper Lipschitzness for multivalued functions introduced by Robinson, and show that this concept ensures local conditioning in the nonconvex case via an abstract subdifferential; in the convex case, we obtain complete characterizations of global conditioning in terms of an extension of the upper-Lipschitz property.
引用
收藏
页码：127 / 148
页数：21
相关论文
共 23 条
[1]  
Martinet B.(1970)Régularisation d'Inéquations Variationelles par Approximations Sucessives Revue Française d'Informatique et de Recherche Opérationnelle 2 154-159
[2]  
Rockafellar R.(1976)Monotone Operators and the Proximal Point Algorithm SIAM Journal on Control and Optimization 14 877-898
[3]  
Zhang R.(1995)Upper-Lipschitz Multifunctions and Inverse Subdifferentials Nonlinear Analysis: Theory, Methods, and Applications 24 273-286
[4]  
Treiman J.(1995)Conditioning Convex and Nonconvex Problems Journal of Optimization Theory and Applications 86 68-123
[5]  
Penot J.(1976)Regularity and Stability for Convex Multivalued Functions Mathematical Operations Research 1 130-143
[6]  
Robinson S.(1994)Bounded Diagonally Stationary Sequences in Convex Optimization Journal of Convex Analysis 1 75-86
[7]  
Lemaire B.(1988)Verifiable Necessary and Sufficient Conditions for Regularity of Set-Valued Maps and Single-Valued Maps Journal of Mathematical Analysis and Applications 134 441-459
[8]  
Borwein J.(1989)Metric Regularity, Openness, and Lipschitz Behavior of Multifunctions Nonlinear Analysis: Theory, Methods, and Applications 13 629-643
[9]  
Zhuang D.(1985)Lipschitz Properties of Multifunctions Nonlinear Analysis: Theory, Methods, and Applications 9 867-885
[10]  
Penot J.(1992)Characterization of Lower Semicontinuous Convex Functions Proceedings of the American Mathematical Society 116 67-72
123