Canonical Duality Approach for Nonlinear Dynamical Systems

Ning Ruan; David Y. Gao

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arXiv · 1206.2447

Canonical Duality Approach for Nonlinear Dynamical Systems

Ning Ruan·David Y. Gao

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Abstract

This paper presents a canonical dual approach for solving a nonlinear population growth problem governed by the well-known logistic equation. Using the finite difference and least squares methods, the nonlinear differential equation is first formulated as a nonconvex optimization problem with unknown parameters. We then prove that by the canonical duality theory, this nonconvex problem is equivalent to a concave maximization problem over a convex feasible space, which can be solved easily to obtain global optimal solution to this challenging problem. Several illustrative examples are presented.

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Ning Ruan, David Y. Gao. 2012-06-12. Canonical Duality Approach for Nonlinear Dynamical Systems. https://arxiv.org/abs/1206.2447

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