  In this paper, it is shown that the solutions of general differentiable
constrained optimization problems can be viewed as asymptotic solutions to sets
of Ordinary Differential Equations (ODEs). The construction of the ODE
associated to the optimization problem is based on an exact penalty formulation
in which the weighting parameter dynamics is coordinated with that of the
decision variable so that there is no need to solve a sequence of optimization
problems, instead, a single ODE has to be solved using available efficient
methods. Examples are given in order to illustrate the results. This includes a
novel systematic approach to solve combinatoric optimization problems as well
as fast computation of a class of optimization problems using analogic circuits
leading to fast, parallel and highly scalable solutions.
