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 ∈ Rn× n is a symmetric
matrix, b ∈ Rn a given vector, and α>0 a real number,
is the optimization problem
\begin{equation*}%\label{TRS}
min\Big{f(x):=1⁄2xTAx+bTx, :,
||x||2 ≤ α2\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" [...]

 

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