Generalized Derivatives for Solutions of Parametric Ordinary Differential Equations with Non-differentiable Right-Hand Sides
Name
10957_2014_539_ReferencePDF.pdf
Size
167.74 KB
Format
Adobe PDF
Checksum (MD5)
5e9e7c8e38d4dbfd7b3daf502ed7f5fb
Author(s)
Khan, Kamil A.
Barton, Paul I.
Date Issued
March 2014
Journal
Journal of Optimization Theory and Applications
Publisher
Springer US
Citation
Khan, Kamil A., and Paul I. Barton. “Generalized Derivatives for Solutions of Parametric Ordinary Differential Equations with Non-Differentiable Right-Hand Sides.” Journal of Optimization Theory and Applications 163.2 (2014): 355–386.
Version
Author's final manuscript
Abstract
Sensitivity analysis provides useful information for equation-solving, optimization, and post-optimality analysis. However, obtaining useful sensitivity information for systems with nonsmooth dynamic systems embedded is a challenging task. In this article, for any locally Lipschitz continuous mapping between finite-dimensional Euclidean spaces, Nesterov’s lexicographic derivatives are shown to be elements of the plenary hull of the (Clarke) generalized Jacobian whenever they exist. It is argued that in applications, and in several established results in nonsmooth analysis, elements of the plenary hull of the generalized Jacobian of a locally Lipschitz continuous function are no less useful than elements of the generalized Jacobian itself. Directional derivatives and lexicographic derivatives of solutions of parametric ordinary differential equation (ODE) systems are expressed as the unique solutions of corresponding ODE systems, under Carathéodory-style assumptions. Hence, the scope of numerical methods for nonsmooth equation-solving and local optimization is extended to systems with nonsmooth parametric ODEs embedded.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Process Systems Engineering Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10957-014-0539-1
