Solution map of a parametric optimization problem
= Solution map of a parametric optimization problem
{title2=$S(a)=\operatorname{argmin}_x F_a(x)$}
The solution map sends a data parameter $a$ to the set of minimizers of the associated objective, $S(a)=\operatorname{argmin}_x F_a(x)$. Existence, uniqueness and local stability are distinct questions. Strong convexity gives uniqueness when a minimizer exists; the <Aubin property> gives a perturbation bound.