  We construct a family of globally defined dynamical systems for a nonlinear
programming problem, such that: (a) the equilibrium points are the unknown (and
sought) critical points of the problem, (b) for every initial condition, the
solution of the corresponding initial value problem converges to the set of
critical points, (c) every strict local minimum is locally asymptotically
stable, (d) the feasible set is a positively invariant set, and (e) the
dynamical system is given explicitly and does not involve the unknown critical
points of the problem. No convexity assumption is employed. The construction of
the family of dynamical systems is based on an extension of the Control
Lyapunov Function methodology, which employs extensions of LaSalle's theorem
and are of independent interest. Examples illustrate the obtained results.
