  We consider an optimal control problem for an abstract nonlinear dissipative
evolution equation. The differential constraint is penalized by augmenting the
target functional by a nonnegative global-in-time functional which is
null-minimized in the evolution equation is satisfied. Different variational
settings are presented, leading to the convergence of the penalization method
for gradient flows, noncyclic and semimonotone flows, doubly nonlinear
evolutions, and GENERIC systems.
