Abstract:
We consider the parametric optimization problem of the following type $$ f(x,y)\longrightarrow min, \; y \in M\subseteq R^m,$$
where $x$ is a parametr from the subset $E\subseteq R^n.$ For this problem a set of $\varepsilon $- points is defined :
$$ a_{\varepsilon }(x)=\{ y \in M: f(x,y)\leq \inf_{y \in M}f(x,y)+\varepsilon \}. $$
The problem of constructing continuous selections of the mapping $a_{\varepsilon }$ is considered. The gradient projection method is used
to construct continuous selections for this multivalued mapping.
