A New Accelerated Algorithm Based on Fixed Point Method for Convex Bilevel Optimization Problems with Applications

Abstract

A new accelerated common fixed point algorithm is introduced and analyzed for a countable family of nonexpansive mappings and then we apply it to solve some convex bilevel optimization problems. Then, under some suitable conditions, we prove a strong convergence result of the proposed algorithm. As an application, we employ the proposed algorithm for regression and classification problems. Moreover, we compare the performance of our algorithm with others. By numerical experiments, we found that our algorithm has a better performance than the others.

Keywords

• bilevel optimization
• fixed point algorithm
• forward-backward algorithm
• regression and classification problems