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

Abstract

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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 ......-ism with ....... Let ......, ....... We prove that the sequence ...... generated by the iterative algorithm ......, ...... converges strongly to ......, where ...... is the minimum-norm solution of the constrained convex minimization problem, which also solves the variational inequality ......, ....... 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.