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Directional Stability Theorem and Directional Metric Regularity

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
arutun{at}orc.ru
izmaf{at}ccas.ru

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. Notes 77 447–460.] 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.

Key Words: metric regularity; Robinson’s constraint qualification; directional regularity; directional metric regularity; feasible arc; sensitivity
History: Received: June 6, 2005; revision received: October 7, 2005;