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Unformatted text preview: 1 + βi pi ), where αi and βi are positive parameters that characterize link i. The second objective (which we
want to minimize) is P = 1T p, the total (transmit) power.
(a) Explain how to ﬁnd the optimal trade-oﬀ curve of total utility and total power, using convex
or quasiconvex optimization.
(b) Plot the optimal trade-oﬀ curve for the problem instance with m = 20, n = 10, Uj (x) = x
for j = 1, . . . , n, pmax = 10, αi = βi = 1 for i = 1, . . . , m, and network topology generated
R = round(rand(m,n));
Your plot should have the total power on the horizontal axis.
16.9 Energy storage trade-oﬀs. We consider the use of a storage device (say, a battery) to reduce the
total cost of electricity consumed over one day. We divide the day into T time periods, and let
pt denote the (positive, time-varying) electricity price, and ut denote the (nonnegative) usage or
consumption, in period t, for t = 1, . . . , T . Without the use of a battery, the total cost is pT u.
Let qt denote the (nonnegative) e...
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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 Berkeley.
- Fall '13
- The Aeneid