The nonsmoothness is viewed by many people as at least an undesirable
(if not unavoidable) property. Our aim here is to show that recent dev
elopments in Nonsmooth Analysis (especially in Exact Penalization Theo
ry) allow one to treat successfully even some quite ''smooth'' problem
s by tools of Nonsmooth Analysis and Nondifferentiable Optimization. O
ur approach is illustrated by one Classical Control Problem of finding
optimal parameters in a system described by ordinary differential equ
ations.