  We consider the problem of minimizing a finite sum of convex functions
subject to the set of minimizers of a convex differentiable function. In order
to solve the problem, an algorithm combining the incremental proximal gradient
method with smooth penalization technique is proposed. We show the convergence
of the generated sequence of iterates to an optimal solution of the
optimization problems, provided that a condition expressed via the Fenchel
conjugate of the constraint function is fulfilled. Finally, the functionality
of the method is illustrated by some numerical experiments addressing image
inpainting problems and generalized Heron problems with least squares
constraints.
