Unformatted text preview: )] for any f : R n ! R and D ³ R n . Now, suppose instead : R ! R is a weakly increasing function, i.e., x > y ) ( x ) ´ ( y ) . Do we still have arg max x 2D f ( x ) = arg max x 2D [ f ( x )]? If yes, prove it; if no, give a counterexample. 4. Give an example of an optimization problem with an in&nite number of solutions (i.e., an in&nite number of maximizer). 5. Find a function f : R ! R and a collection of sets S k ³ R such that f attains a maximum on each of S k , but not on [ 1 k =1 S k . 1...
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 Spring '11
 Siyang
 Economics, Optimization, Monotonic function, Convex function

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