Abstract
When modeling the interaction between several agents, each trying to achieve some objective, we often need to express their dependence using a mixture of equations, inequalities and more general inclusions. Even for minimization problems, we’ve seen that solutions can be characterized, at least in part, by inclusions derived from the Fermat rule and the Rockafellar condition.
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.
A mapping \(H:\mathbb {R}^n\rightarrow \mathbb {R}^n\) is continuously invertible near \(\bar{x}\) if there are neighborhoods C and D of \(\bar{x}\) and \(H(\bar{x})\), respectively, such that the restriction of H to C produces a bijective mapping \(H:C\rightarrow D\) and its inverse mapping \(H^{-1}:D\rightarrow C\) is continuous.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Royset, J.O., Wets, R.JB. (2021). GENERALIZED EQUATIONS. In: An Optimization Primer. Springer Series in Operations Research and Financial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-76275-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-76275-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-76274-2
Online ISBN: 978-3-030-76275-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)