2018/01/26 by Ning Ruan, Ruan, Ning, David Yang Gao +1
Computer Science · Engineering · #Contact Mechanics and Variational Inequalities #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1801.08651
openalex publication_date 2018/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness is discussed based on objectivity principle in continuum physics; then the canonical duality theory is applied for solving this problem to obtain not only all fixed points, but also their stability properties. Applications are illustrated by challenging problems governed by nonconvex polynomial, exponential, and logarithmic operators. This paper shows that within the framework of the canonical duality theory, there is no difference between the fixed point problems and nonconvex analysis/optimization in multidisciplinary studies.