title: Regularized gradient-projection methods for finding the minimum-norm solution of the constrained convex minimization problem.
abstract: LetHbe a real Hilbert space andCbe a nonempty closed convex subset ofH. Assume thatgis a real-valued convex function and the gradient ∇gis [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.
authors.affiliation: College of Science, Civil Aviation University of China, Tianjin, 300300 China ; Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin, 300300 China.
authors.forename: Ming
authors.initials: M
authors.lastname: Tian
authors.affiliation: College of Science, Civil Aviation University of China, Tianjin, 300300 China.
authors.forename: Hui-Fang
authors.initials: HF
authors.lastname: Zhang
keywords: minimum-norm; regularized gradient-projection method; the constrained convex minimization problem; variational inequality