Show the following results on the subdifferential. (a) Let fe r (R) and g(x) = f(x)...

 

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Show the following results on the subdifferential. (a) Let fe rº (R") and g(x) = f(x) with > 0. Show that Og(x) = 00 f(x) for any a € R". (b) Let f, g € Iº (R") and h = f + g. Show that Of(x) + g(x) ≤ Əh(x). (c) Show that sgn(x) = ||||1, where sgn() is the sign function. Show the following results on the subdifferential. (a) Let fe rº (R") and g(x) = f(x) with > 0. Show that Og(x) = 00 f(x) for any a € R". (b) Let f, g € Iº (R") and h = f + g. Show that Of(x) + g(x) ≤ Əh(x). (c) Show that sgn(x) = ||||1, where sgn() is the sign function.