Hölder Stable Minimizers, Tilt Stability, and Hölder metric Regularity of Subdifferentials

2015 ◽  
Vol 25 (1) ◽  
pp. 416-438 ◽  
Author(s):  
Xi Yin Zheng ◽  
Kung Fu Ng
Keyword(s):  
Metric Regularity ◽  
Hölder Metric ◽  
Tilt Stability ◽  
Hölder Metric Regularity

Hölder metric regularity of set-valued maps

2010 ◽  
Vol 132 (1-2) ◽  
pp. 333-354 ◽  
Author(s):  
Hélène Frankowska ◽  
Marc Quincampoix
Keyword(s):  
Metric Regularity ◽  
Hölder Metric ◽  
Hölder Metric Regularity

scholarly journals Directional Hölder Metric Regularity

2015 ◽  
Vol 171 (3) ◽  
pp. 785-819 ◽  
Author(s):  
Huynh Van Ngai ◽  
Nguyen Huu Tron ◽  
Michel Théra
Keyword(s):  
Metric Regularity ◽  
Hölder Metric ◽  
Hölder Metric Regularity

A general metric regularity in asplund banach spaces

1998 ◽  
Vol 19 (3-4) ◽  
pp. 215-226 ◽  
Author(s):  
T. Amahroq ◽  
A. Jourani ◽  
L. Thibault
Keyword(s):  
Banach Spaces ◽  
Metric Regularity

Statistical Inference of Second-Order Cone Programming

2019 ◽  
Vol 36 (02) ◽  
pp. 1940003
Author(s):  
Liwei Zhang ◽  
Shengzhe Gao ◽  
Saoyan Guo
Keyword(s):  
Lipschitz Continuity ◽  
Metric Regularity ◽  
Optimal Solution ◽  
Second Order ◽  
Lipschitz Continuous ◽  
Set Valued Mapping ◽  
Second Order Cone ◽  
Degeneracy Condition ◽  
Optimal Solution Set ◽  
The Stability

In this paper, we study the stability of stochastic second-order programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the feasible set-valued mapping, the outer semicontinuity of the optimal solution set and Lipschitz continuity of optimal values are demonstrated. Moreover, we prove that, if the constraint non-degeneracy condition and strong second-order sufficient condition hold at a local minimum point of the original problem, there exists a Lipschitz continuous solution path satisfying the Karush–Kuhn–Tucker conditions.

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