Parametric optimization

A parametric optimization problem has objective or constraints depending on input data. Its optimizer set is a solution map of a parametric optimization problem. Sensitivity analysis asks how this map changes as the data vary.

The solution map sends a data parameter $a$ to the set of minimizers of the associated objective, $S(a)={\mathrm{argmin}}_x{F}_a(x)$. Existence, uniqueness and local stability are distinct questions. Strong convexity gives uniqueness when a minimizer exists; the Aubin property gives a perturbation bound.