Stability of generalized equations under nonlinear perturbations
type: Item
instance of: scholarly article
title: Stability of generalized equations under nonlinear perturbations
zbMATH Open document ID: 1427.90279
author: Nguyen Thanh Qui
author: Hoang Ngoc Tuan
published in: Optimization Letters
publication date: 2018-08-03T00:00:00Z
review text: The aim of this paper is to investigate solution stability of generalized equations over polyhedral convex sets. Based on the results of Mordukhovich and Rockafellar on the chain rules for partial second-order subdifferentials, an exact formula for computing the Mordukhovich coderivative of the normal cone operator to nonlinearly perturbed polyhedral convex sets is obtained. This formula leads to an upper estimate for the values of the Mordukhovich coderivative of the solution map. Finally, a sufficient condition for the local Lipschitz-like property of the solution map of the generalized equations under nonlinear perturbations is derived.
reviewed by: Samir Kumar Neogy
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 6912895
zbMATH Keywords: generalized equation
zbMATH Keywords: nonlinear perturbation
zbMATH Keywords: local Lipschitz-like property
zbMATH Keywords: normal cone mapping
zbMATH Keywords: coderivative
zbMATH Keywords: partial second-order subdifferential
MaRDI profile type: Publication
full work available at URL: s11590-017-1147-4
OpenAlex ID: W2610272642
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DOI: 10.1007/S11590-017-1147-4
description: scientific article; zbMATH DE number 6912895