Abstract
The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. Based on the viscosity approximation method, we combine the GPA and averaged mapping approach to propose implicit and explicit composite iterative algorithms for finding a common solution of an equilibrium and a constrained convex minimization problem for the first time in this paper. Under suitable conditions, strong convergence theorems are obtained. MSC:46N10, 47J20, 74G60.
Highlights
Let H be a real Hilbert space with inner product ·, · and norm ·
He proved that the sequences {xn} converge strongly to a minimizer of the constrained convex minimization problem, which solves a certain variational inequality
Based on the viscosity approximation method, we combine the gradient-projection algorithm (GPA) and averaged mapping approach to propose implicit and explicit composite iterative method for finding the common element of the set of solutions of an equilibrium problem and the solution set of a constrained convex minimization problem
Summary
Let H be a real Hilbert space with inner product ·, · and norm ·. Given a mapping F : C → H, let φ(x, y) = Fx, y – x for all x, y ∈ C, z ∈ EP(φ) if and only if Fz, y – z ≥ for all y ∈ C, that is, z is a solution of the variational inequality.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
