C Cxg O. C be a convex set, and ⌅ C be its indicator function •For x ⌘/ C, ⌅ C (x)= Ø (by convention) •For x ⌘ C, we have g ⌘ ⌅ C (x)i ff ⌅ C (z) ≥ ⌅ C (x) g (z −x), z ⌘ C, or equivalently g (z − x) ⌥ 0 for all z ⌘ C Thus ⌅ C (x) is the normal cone of C at x, denoted N C (x) N C (x)= g g (z x) 0, z C. $ õ º ó/ z ( D Ø b _ ° _6õ M >%± } O \&k c º v ¥6ä & b v)~ z _ > 8 Z $ õ º ó/ z ( D Ø b _ ° j g _ $ õ º ó/ z ( b4E õ _ X 8 Z ô1 K r K S b >%± } O K r M 0° $ õ º ó/ z ( _ ° b >%± } O >&>/>' $ õ º ó/ z ( D Ø b _ ° b% $× ¥ î Ï Þ î º Â ¼ å « I ì @ Ó u } p v)~ z X b P ö &k ¥ v)~ z "á b ¥ V'¼ _ ~ v)~ z b q ö ì x% %i µ I ì W M » ó/ b "á ì.
Approximation Algorithms For Stochastic Optimization Ppt Download from Approximation Algorithms for Stochastic ...
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