Stability of generalized equations under nonlinear perturbations

Abstract

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.

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Acknowledgements

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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Correspondence to Nguyen Thanh Qui.

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Qui, N.T., Tuan, H.N. Stability of generalized equations under nonlinear perturbations. Optim Lett 12, 799–815 (2018). https://doi.org/10.1007/s11590-017-1147-4

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Keywords

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