- Title
- Canonical duality approach for non-linear dynamical systems
- Creator
- Ruan, Ning; Gao, David
- Date
- 2014
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/67307
- Identifier
- vital:5884
- Identifier
-
https://doi.org/10.1093/imamat/hxs067
- Identifier
- ISSN:1464-3634
- Abstract
- This paper presents a canonical dual approach for solving a non-linear population growth problem governed by the well-known logistic equation. Using the finite difference and least squares methods, the non-linear differential equation is first formulated as a non-convex optimization problem with unknown parameters. We then prove that by the canonical duality theory, this non-convex problem is equivalent to a concave maximization problem over a convex feasible space, which can be solved easily to obtain a global optimal solution to this challenging problem. Several illustrative examples are presented.
- Publisher
- Oxford University Press
- Relation
- IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) Vol. 79, no. 2 (2014), p. 313-325
- Rights
- © The authors 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
- Rights
- This metadata is freely available under a CCO license
- Subject
- Canonical duality theory; Discrete dynamical systems; Global optimization; Least squares method; Logistic equation
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