Suppose we are given two distributions of random variables that take values in the support set {1, . , n}: (j and (j, with both vectors nonnegative...
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This is a question of

convex optimization, could anyone help me with that?

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Suppose we are given two distributions of random variables that take values in the
support set {1, . . . , n}: (j and (j, with both vectors nonnegative and adding up to one. We
would like to find a sequence of K distributions on the same support set that gradually “transforms” (j into Q”. That is, we would like to find pk E R", k = 1, . . . , K, such that each pk is a valid distribution vector, p1 = (j, 33K : Q', and pk m pk“, i.e., we want to minimize
K—1
2 MW“),
k:1
for some metric p. For each of the metrics below, explain how you would use convex
optimization to solve the problem:
i- 910“: v) = llu - ’Ullg
ii- 1020“,”) = SLR/Um" — W72"?
iii- 93015:”) = max,:1,._,,n 23:1 “3' — 22:1 ”3' In the case of metric p1, you should also be able to explicitly characterize the optimal
solution 7 please give the formulae and justify your answer.

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