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 solvingbi-level convex optimization problems in Hilbert spaces in the form of the minimizationof smooth and strongly convex function over the optimal solutions set which is the setof all minimizers of the sum of smooth and nonsmooth functions. In addition, we applyour algorithms to solve regression and classification problems by using machine learningmodels. Our experiments show that our proposed machine learning algorithm has a betterconvergence behaviour than the others.