- Title
- On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications
- Creator
- Ruan, Ning; Gao, David
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/166961
- Identifier
- vital:13543
- Identifier
-
https://doi.org/10.1186/s13663-018-0648-x
- Identifier
- ISBN:1687-1820
- Abstract
- This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e., the general fixed point problem is first reformulated as a nonconvex optimization problem, its well-posedness is discussed based on the objectivity principle in continuum physics; then the canonical duality theory is applied for solving this challenging problem to obtain not only all fixed points, but also their stability properties. Applications are illustrated by 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.
- Publisher
- Springer International Publishing
- Relation
- Fixed Point Theory and Applications Vol. 2018, no. 1 (2018), p. 1-19
- Rights
- http://creativecommons.org/licenses/by/4.0/
- Rights
- Copyright © 2018, The Author(s).
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0101 Pure Mathematics; 0102 Applied Mathematics; Canonical duality theory; Fixed point; Mathematical modeling; Multidisciplinary studies; Nonconvex optimization; Properly-posed problem
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