bv_cvxbook_extra_exercises

# In the basic power ow optimization problem we choose

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Unformatted text preview: ation problem minimize nλmax (L(W ) + diag(x)) subject to 1T x = 0, with variable x ∈ Rn . Express this problem as an SDP. (d) Derive an alternative expression for f (W ), by taking the dual of the SDP in part 3. Show that the dual SDP is equivalent to the following problem: maximize i≤ j subject pi wij pi − pj 2 = 1, 2 2 i = 1, . . . , n, with variables pi ∈ Rn , i = 1, . . . , n. In this problem we place n points pi on the unit sphere in Rn in such a way that the weighted sum of their squared pair-wise distances is maximized. 15.3 Utility versus latency trade-oﬀ in a network. We consider a network with m edges, labeled 1, . . . , m, and n ﬂows, labeled 1, . . . , n. Each ﬂow has an associated nonnegative ﬂow rate fj ; each edge or link has an associated positive capacity ci . Each ﬂow passes over a ﬁxed set of links (its route); the total traﬃc ti on link i is the sum of the ﬂow rates over all ﬂows that pass through link i. The ﬂow routes are described by a routing matrix R ∈ Rm×n , de...
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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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