Regularized gradient-projection methods for finding the minimum-norm solution of the constrained convex minimization problem

Let H be a real Hilbert space and C be a nonempty closed convex subset of H. Assume that g is a real-valued convex function and the gradient ∇g is [Formula: see text]-ism with [Formula: see text]. Let [Formula: see text], [Formula: see text]. We prove that the sequence [Formula: see text] generated by the iterative algorithm [Formula: see text], [Formula: see text] converges strongly to [Formula: see text], where [Formula: see text] is the minimum-norm solution of the constrained convex minimization problem, which also solves the variational inequality [Formula: see text], [Formula: see text]. Under suitable conditions, we obtain some strong convergence theorems. As an application, we apply our algorithm to solving the split feasibility problem in Hilbert spaces.