bv_cvxbook_extra_exercises

You can think of ui as representing a deviation of

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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.

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