**Thursday, 14:15 - 14:40 h, Room: H 2051**

**Nguyen Dong Yen**

Coderivatives of a Karush-Kuhn-Tucker point set map and applications

**Coauthor: Gue Myung Lee**

**Abstract:**

*The trust-region subproblem* corresponding to the triple

*{A,b,α}*, where *A ∈ ***R**^{n× n} is a symmetric

matrix, *b ∈ ***R**^{n} a given vector, and *α>0* a real number,

is the optimization problem

\begin{equation*}%\label{TRS}

min\Big{f(x):=1⁄2x^{T}Ax+b^{T}x, :,

||x||^{2} ≤ α^{2}\Big}.\eqno{(P)}

\end{equation*} One often encounters with *(P)* in

the development of trust-region methods for nonlinear programs.

Since the feasible region of *(P)* is a convex compact set with an

infinite number of extreme points, the structure of its solution set

(resp. of its Karush-Kuhn-Tucker point set) is quite different from

that of quadratic programs with linear constraints. By using some

tools from Variational Analysis, this paper investigates the

stability of *(P)* with respect to the perturbations of all the

three components of its data set *{A,b,α}*.

Talk 3 of the invited session Thu.2.H 2051

**"Variational analysis of optimal value functions and set-valued mappings with applications"** [...]

Cluster 24

**"Variational analysis"** [...]