Abstract
This chapter starts with some brief historical overview of optimization followed by four subsections devoted to the formulation and reformulation of optimization problems. The subsequent two sections revisit basic tools of mathematical analysis and matrix analysis, which will be frequently used along the book. Next we revisit the local optimality conditions for functions of several variables (also called multivariate) at interior points of their domains that are usually studied in courses on differential calculus. Then we introduce the concept of coercive function, which is used to prove the existence of global minimum of continuous functions on unbounded domains.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
J.M. Borwein, personal communication, January 2016.
- 2.
Private communication of the note Optimisation versus Optimisme, sent by J.-B. Hiriart-Urruty to the group SMAI-MODE in February 2014.
- 3.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Aragón, F.J., Goberna, M.A., López, M.A., Rodríguez, M.M.L. (2019). Preliminaries. In: Nonlinear Optimization. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-11184-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-11184-7_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11183-0
Online ISBN: 978-3-030-11184-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)