TITLE:
Convergence Rate Analysis of Modified BiG-SAM for Solving Bi-Level Optimization Problems Based on S-FISTA
AUTHORS:
Nishi Xiaoyin, Lin Yang
KEYWORDS:
Bi-Level Optimization, Convex Problems, First-Order Methods, Proximal Gradient Method, Sequential Averaging Method, Moreau Envelope
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.4,
April
27,
2025
ABSTRACT: In this paper, we consider a more general bi-level optimization problem, where the inner objective function is consisted of three convex functions, involving a smooth and two non-smooth functions. The outer objective function is a classical strongly convex function which may not be smooth. Motivated by the smoothing approaches, we modify the classical bi-level gradient sequential averaging method to solve the bi-level optimization problem. Under some mild conditions, we obtain the convergence rate of the generated sequence, and then based on the analysis framework of S-FISTA, we show the global convergence rate of the proposed algorithm.