![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
ABSTRACT
We explore how to build a vector field from the various functions involved in a given mathematical programme, and show that equilibria of the corresponding dynamical system are precisely the solutions of the underlying optimality conditions for the original optimization problem. The general situation in which explicit inequality constraints are present is especially interesting as the vector field has to be discontinuous, and so one is led to consider discontinuous dynamical systems and their equilibria.
Acknowledgments
Special thanks to several referees whose criticism helped towards the final form of this work.
Disclosure statement
No potential conflict of interest was reported by the author.
Additional information
Funding
Research supported in part by MTM2013-47053-P of the MINECO (Spain), Secretaría de Estado de Investigación, Desarrollo e Innovación, PEII-2014-010-P of the Conserjera de Cultura (JCCM), and by GI20152919 of UCLM.