Don't understand this statement: 'Note that G(w, α) is convex in w and linear, hence concave, in α'
I am not sure how this conclusion is drawn in the Lecture 7 SVM:
"Note that G(w, α) is convex in w and linear, hence concave, in α"
why does being convex in w and linear imply concave in alpha?
Hello,
The sentence must be read as:
For a fixed \( \alpha \), \( w \mapsto G(w, \alpha) \) is convex in \( w \).
For a fixed \( w \), \( \alpha \mapsto G(w, \alpha) \) is affine in \( \alpha \), and hence concave in \( \alpha \).
Is this clear ?
Best,
Scott
Don't understand this statement: 'Note that G(w, α) is convex in w and linear, hence concave, in α'
I am not sure how this conclusion is drawn in the Lecture 7 SVM:
"Note that G(w, α) is convex in w and linear, hence concave, in α"
why does being convex in w and linear imply concave in alpha?
Thanks for your help
Hello,
The sentence must be read as:
For a fixed \( \alpha \), \( w \mapsto G(w, \alpha) \) is convex in \( w \).
For a fixed \( w \), \( \alpha \mapsto G(w, \alpha) \) is affine in \( \alpha \), and hence concave in \( \alpha \).
Is this clear ?
Best,
Scott
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