One particularly important class of equilibrium problems which has aided in the rise of projected dynamical systems has been that of variational inequalities.
However, similar concepts can be found in the mathematical literature which predate this, especially in connection with variational inequalities and differential inclusions.
This desired result is achieved through the use of projection operators and two particular important classes of convex cones.
This differential equation can be alternately characterized by or The convention of denoting the vector field -F with a negative sign arises from a particular connection projected dynamical systems shares with variational inequalities.
The convention in the literature is to refer to the vector field as positive in the variational inequality, and negative in the corresponding projected dynamical system.