17 research outputs found
Generalized Forward-Backward Splitting with Penalization for Monotone Inclusion Problems
We introduce a generalized forward-backward splitting method with penalty
term for solving monotone inclusion problems involving the sum of a finite
number of maximally monotone operators and the normal cone to the nonempty set
of zeros of another maximal monotone operator. We show weak ergodic convergence
of the generated sequence of iterates to a solution of the considered monotone
inclusion problem, provided the condition corresponded to the Fitzpatrick
function of the operator describing the set of the normal cone is fulfilled.
Under strong monotonicity of an operator, we show strong convergence of the
iterates. Furthermore, we utilize the proposed method for minimizing a
large-scale hierarchical minimization problem concerning the sum of
differentiable and nondifferentiable convex functions subject to the set of
minima of another differentiable convex function. We illustrate the
functionality of the method through numerical experiments addressing
constrained elastic net and generalized Heron location problems