Exact Penalty in Constrained Optimization

Alexander J. Zaslavski ()
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Alexander J. Zaslavski: Technion - Israel Institute of Technology

Chapter 2 in Optimization on Metric and Normed Spaces, 2010, pp 11-79 from Springer

Abstract: 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 $$B(x,r) = \{ y \in X:||y - x|| \leq r\},\ B_ {\ast} (x^{\ast},r) = \{ l \in X^ {\ast} :||l - x^ {\ast}||^{\ast} \leq r\}.$$

Date: 2010
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DOI: 10.1007/978-0-387-88621-3_2

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