ACCELERATED FIXED POINT ALGORITHM FOR CONVEX BI-LEVEL OPTIMIZATION PROBLEMS IN HILBERT SPACES WITH APPLICATIONS

Abstract

In this thesis, we propose and analyze a new accelerated algorithm for solving bi-level convex optimization problems in Hilbert spaces in the form of the minimization of smooth and strongly convex function over the optimal solutions set which is the set
of all minimizers of the sum of smooth and nonsmooth functions. In addition, we apply our algorithms to solve regression and classification problems by using machine learning models. Our experiments show that our proposed machine learning algorithm has a better convergence behaviour than the others.