Gradient projection method and continuous selections of multivalued mappings

Abstract

We consider the parametric optimization problem of the following type
f(x, y) −→ min, y ∈ M ⊆ R
m,
where x is a parametr from the subset E ⊆ Rn.
For this problem a set of ε - points is defined :
aε(x) = {y ∈ M : f(x, y) ≤ inf
y∈M
f(x, y) + ε}.
The problem of constructing continuous selections of the mapping aε is considered. The gradient projection method is used to
construct continuous selections for this multivalued mapping