  We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in
real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a
cocoercive operator and $C$ the nonempty set of zeros of another cocoercive
operator. We propose a forward-backward penalty algorithm for solving this
problem which extends the one proposed by H. Attouch, M.-O. Czarnecki and J.
Peypouquet in [3]. The condition which guarantees the weak ergodic convergence
of the sequence of iterates generated by the proposed scheme is formulated by
means of the Fitzpatrick function associated to the maximally monotone operator
that describes the set $C$. In the second part we introduce a
forward-backward-forward algorithm for monotone inclusion problems having the
same structure, but this time by replacing the cocoercivity hypotheses with
Lipschitz continuity conditions. The latter penalty type algorithm opens the
gate to handle monotone inclusion problems with more complicated structures,
for instance, involving compositions of maximally monotone operators with
linear continuous ones.
