Abstract
Let \((X,||\cdot ||)\) be a Banach space and \(\left(X^{\ast},||\cdot ||_{\ast}\right)\) its dual space. For each \(x\ \in\ X,\) each \(x^{\ast}\ \in\ X^{\ast}\) and each r > 0 set \(B(x,r) = \{ y \in X:||y - x|| \leq r\},\ B_ {\ast} (x^{\ast},r) = \{ l \in X^ {\ast} :||l - x^ {\ast}||^{\ast} \leq r\}.\)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Zaslavski, A.J. (2010). Exact Penalty in Constrained Optimization. In: Optimization on Metric and Normed Spaces. Springer Optimization and Its Applications, vol 44. Springer, New York, NY. https://doi.org/10.1007/978-0-387-88621-3_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-88621-3_2
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-88620-6
Online ISBN: 978-0-387-88621-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)