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Yamada, I., Yukawa, M. and Yamagishi, M. (2011) Minimizing the Moreau Envelope of Nonsmooth Convex Functions over the Fixed Point Set of Certain Quasi-Nonexpansive Mappings. In: Bauschke, H., Burachik, R., Combettes, P., Elser, V., Luke, D. and Wolkowicz, H., Eds., Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer, 345-390.
https://doi.org/10.1007/978-1-4419-9569-8_17

has been cited by the following article:

• 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.