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Unformatted text preview: nomial, evaluated at a weighted geometric mean of two points, is no
more than the weighted geometric mean of the posynomial evaluated at the two points. 3.24 CVX implementation of a concave function. Consider the concave function f : R → R deﬁned by
f (x) = (x + 1)/2 x > 1
√
x
0 ≤ x ≤ 1, with dom f = R+ . Give a CVX implementation of f , via a partially speciﬁed optimization problem.
Check your implementation by maximizing f (x) + f (a − x) for several interesting values of a (say,
a = −1, a = 1, and a = 3).
3.25 The following optimization problem arises in portfolio optimization:
rT x + d
Rx + q 2 maximize
subject to n
i=1 x fi ( x i ) ≤ b
c. The variable is x ∈ Rn . The functions fi are deﬁned as fi (x) = αi xi + βi xi  + γi xi 3/2 , with βi > αi , γi > 0. We assume there exists a feasible x with rT x + d > 0. Show that this problem can be solved by solving an SOCP (if possible) or a sequence of SOCP
feasibility problems (otherwise).
23 3.26 Positive nonconvex QCQP. W...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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