- Computation of Graphical Derivative for a Class of Normal Cone Mappings under a Very Weak Condition Huy Chieu Nguyen(nghuychieugmail.com) Van Hien Le(lehiendhvgmail.com) Abstract: Let $\Gamma:=\{x\in \R^n\, |\, q(x)\in\Theta\},$ where $q: \R^n\rightarrow\R^m$ is a twice continuously differentiable mapping, and $\Theta$ is a nonempty polyhedral convex set in $\R^m.$ In this paper, we first establish a formula for exactly computing the graphical derivative of the normal cone mapping $N_\Gamma:\R^n\rightrightarrows\R^n,$ $x\mapsto N_\Gamma(x),$ under the condition that $M_q(x):=q(x)-\Theta$ is metrically subregular at the reference point. Then, based on this formula, we exhibit formulae for computing the graphical derivative of solution mappings and present characterizations of the isolated calmness for a broad class of generalized equations. Finally, applying to optimization, we get a new result on the isolated calmness of stationary point mappings. Keywords: Computation, Graphical Derivative, Normal Cone Mapping, Generalized Equation, Isolated Calmness Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Download: [PDF]Entry Submitted: 03/29/2016Entry Accepted: 03/29/2016Entry Last Modified: 03/29/2016Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.