A NEW SPLITTING FORWARD-BACKWARD ALGORITHM AND CONVERGENCE FOR SOLVING CONSTRAINED CONVEX OPTIMIZATION PROBLEM IN HILBERT SPACES

The purposes of this paper are to introduce and study a new splitting forward-backward algorithm with penalization terms along with its convergence behavior. Under observing some available properties of some monotone type operators together with the appropriate scalar terms, it allows us to create a new inertial algorithm which is called the new splitting forward-backward algorithm (NSFB) for solving monotone inclusion problems concerning the sum of the maximally monotone operator and the normal cone to the nonempty set of zeros of another maximally monotone operator. The obtained main results can be applied to solve some constrained convex minimization problems of the sum of two functions with certain conditions. Furthermore, we also provide a numerical example of the method through numerical experiments addressing constrained convex minimization problems.