Work

Second-order dynamical system to solve the sum of monotone operators via the KM algorithm

Year: 2025

Type: article

Abstract: Dynamical systems serve as powerful tools for studying optimization and fixed-point algorithms. Motivated by this perspective, we take a problem to find solution of the form 0 ∈ A ( y ) + B ( y ) in Hilbert spaces using a dynamical system approach based on the Krasnoselskii–Mann method, where A is a set-valued operator, while B is a single-valued operator. Specifically, we propose a second-order dynamical system that arises as the continuous limit of the Krasnoselskii–Mann algorithm and analyze its stability using a Lyapunov function. We also conduct numerical applications to complement the theoretical analysis and visualize the system’s behavior through graphical representations, which enhance the understanding of the inclusion problem. Furthermore, we extend our study by deriving a novel dynamical system using the heavy ball method.

Source: Alexandria Engineering Journal

DOI: 10.1016/j.aej.2025.03.040

Authors: Yang Cao, Vajahat Karim Khan, Mohd. Sarfaraz, Adnène Arbi, Md. Kalimuddin Ahmad

Institutions: Southeast University, Aligarh Muslim University, Jaypee Institute of Information Technology, University of Carthage, Tunisia Polytechnic School

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,900

Funders: National Natural Science Foundation of China, Natural Science Foundation of Jiangsu Province