Structural stability of vector optimization problems

Paulo Mbunga
We study global stability properties for vector optimization problems of the type: \begin{align} \tag*{$\mathcal{VOP}(f,H,G)$:} \min\left\{f(x)=\left(f_1(x),\dots,f_l(x)\right) \mid x\in M[H,G]\right\}, \end{align} where \begin{align*} M[H,G]:=\left\{x\in \R^n\mid h_i(x)=0,\quad g_j(x)\leq 0, \quad i\in I,j\in J\right\} \end{align*} with \begin{alignat*}{3} I &:= \{1,\dots,m\}, &\quad J &:= \{1,\dots,s\},&\quad L&:=\{1,\dots,l\}. \end{alignat*} We extend Guddat/Jongen's \cite{structstab} concept of structural stability of scalar nonlinear optimization problems to vector optimization problems. Under the assumption that $M[H,G]$ is compact we prove the necessary condition for the structural stability...
This data repository is not currently reporting usage information. For information on how your repository can submit usage information, please see our documentation.