Fixed point iterative algorithm in convex optimizationproblem

The aim of this thesis is to approach to a solution of convex minimization problem with a new gradient projection algorithm. For this purpose, averaged mapping approach which was proposed by Xu [1] as an alternative to solve the convex minimization problem has been used. The new gradient projection algorithm proposed in this thesis is based on Noor iteration method [2]. In the first part of this thesis, the subject handled in the thesis has been introduced in general terms. In the second part, a brief literature summary of the topic of the thesis has been given. In the third part, some basic concepts have been given to make the thesis understandable. In the fourth section, materials and methods that enable us to realize the purpose of the thesis and Xu's an averaged mapping approach to show weakly convergence to a solution of the convex minimization problem have been explained. In the fifth chapter, it has been shown that the new projection algorithm we propose is weakly convergent to solution of the convex minimization problem. Also, it has been given an example in infinite dimensional Hilbert space to support the result that we proved it. Finally, in the sixth chapter of the thesis, the results of the thesis have been discussed and some suggestions have been made.