Directional Stability Theorem and Directional Metric Regularity

Authors:
Aram V. Arutyunov;Alexey F. Izmailov
Affiliations:
Peoples Friendship University, Miklukho-Maklaya Str. 6, 117198 Moscow, Russia;Faculty of Computational Mathematics and Cybernetics, Department of Operations Research, Moscow State University, Leninskiye Gori, GSP-2, 119992 Moscow, Russia
Venue:
Mathematics of Operations Research
Year:
2006

Citing 4
Cited 0

Directional derivatives of optimal solutions in smooth nonlinear programming

Journal of Optimization Theory and Applications
Differential characterizations of covering, metric regularity, and Lispchitzian properties of multifunctions between Banach spaces

Nonlinear Analysis: Theory, Methods & Applications
Perturbed Optimization in Banach spaces I: A General Theory based on a Weak Directional Constraint Qualification

SIAM Journal on Control and Optimization
Perturbed Optimization in Banach spaces II: A Theory based on a Strong Directional Constraint Qualification

SIAM Journal on Control and Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We develop a new regularity concept, unifying metric regularity, Robinson's constraint qualification, and directional regularity. We present the directional stability theorem and the related concept of directional metric regularity. On one hand, our directional stability theorem immediately implies Robinson's stability theorem [Arutyunov, A. V. 2005. Covering of nonlinear maps on cone in neighborhood of abnormal point. Math. Notes77 447--460.] as a particular case, while on the other hand, our theorem easily implies various stability results under the directional regularity condition, widely used in sensitivity analysis. Some applications of this kind are also presented.