Abstract
We show that suitable restatements of the classical Weierstrass extreme value theorem give necessary and sufficient conditions for the existence of a global minimum and of both a global minimum and a global maximum.
This is a preview of subscription content, log in via an institution to check access.
References
Ioffe, A., Lucchetti, R.E.: Generic well-posedness in minimization problems. Abstr. Appl. Anal. 4, 343–360 (2005)
Willard, S.: General Topology. Addison-Wesley, Reading (1970)
Acknowledgments
I am grateful to Maxim I. Todorov for his helpful and stimulating comments. Thanks are also due to an anonymous referee for his/her careful report, pointing out some important corrections and observing that the conditional completeness assumption on \(C\) made in the initial version was superfluous. The author has been supported by the MICINN of Spain, Grant MTM2011-29064-C03-01. He is affiliated to MOVE (Markets, Organizations and Votes in Economics).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Martínez-Legaz, J.E. On Weierstrass extreme value theorem. Optim Lett 8, 391–393 (2014). https://doi.org/10.1007/s11590-012-0587-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-012-0587-0