A Fast Forward-Backward Algorithm Using Linesearch and Inertial Techniques for Convex Bi-level Optimization Problems with Applications

In this research, we study convex bi-level optimization problems for which the inner level consists of the sum of two proper, convex, and lower semi-continuous functions. We propose and analyze a new accelerated forward-backward algorithm using linesearch and inertial techniques for solving a solution of convex bi-level optimization. We then establish a strong convergence theorem of the proposed method under some suitable conditions. As an application, we apply our algorithm to solving data classifications of some non-communicable diseases. We conduct a comparative analysis with existing algorithms to show the effectiveness of our algorithm. Our numerical experiments confirm that our proposed algorithm outperforms other methods in the literature.