423
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Optimisation and asymptotic stability

&
Pages 2404-2410 | Received 26 Apr 2016, Accepted 28 Oct 2016, Published online: 23 Nov 2016
 

ABSTRACT

The problems of unconstrained optimisation and establishing asymptotic stability have much in common. Understanding the analogy between these two sheds light on their interconnection and may lead to a number of new results. For instance, in this paper, we provide estimates of the rate of convergence when analysing asymptotic stability of differential equations, rather than just ascertain the very fact of stability. Also, standard methods for the design of Lyapunov functions (e.g. those having the meaning of the full energy of the system) turn out to be unsatisfactory from this point of view and have to be modified. These claims are exemplified in the paper by considering the heavy-ball method for function minimisation ‘in parallel’ with the problem of asymptotic stability for the synchronous motor equation.

Acknowledgment

The authors would like to thank Denis Efimov for his interest in the subject of the paper, suggestions and references to the literature. Help of Yana Kvinto in performing numerical experiments is also appreciated.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The financial support for this work was provided by the Russian Science Foundation [grant number 16-11-10015].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.