NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES

Nguyễn Thành Quí

Abstract


This paper establishes an upper estimate for the Frechet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the result leads to an upper estimate for values of the Mordukhovich coderivative of such mappings. On the basis, new results on solution stability of parametric affine variational inequalities under nonlinear perturbations are derived.


Keywords


Polyhedral normal cone mapping; Nonlinear perturbation; Frechet normal cone; Limiting normal cone; Mordukhovich coderivative; Estimate; Parametric affine variational inequality



DOI: http://dx.doi.org/10.37569/DalatUniversity.2.3.208(2012)

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