Optimization Letters

, Volume 12, Issue 4, pp 799–815 | Cite as

Stability of generalized equations under nonlinear perturbations

  • Nguyen Thanh QuiEmail author
  • Hoang Ngoc Tuan
Original Paper


This paper studies solution stability of generalized equations over polyhedral convex sets. An exact formula for computing the Mordukhovich coderivative of normal cone operators to nonlinearly perturbed polyhedral convex sets is established based on a chain rule for the partial second-order subdifferential. This formula leads to a sufficient condition for the local Lipschitz-like property of the solution maps of the generalized equations under nonlinear perturbations.


Generalized equation Nonlinear perturbation Local Lipschitz-like property Normal cone mapping Coderivative Partial second-order subdifferential 



This work was done when the authors were working at the Vietnam Institute for Advanced Study in Mathematics (VIASM). The authors would like to thank the VIASM for hospitality and kind support.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Information and Communication TechnologyCan Tho UniversityCan ThoVietnam
  2. 2.Department of MathematicsHanoi Pedagogical University 2Phuc YenVietnam

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