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Unformatted text preview: use the following rules:
• Bisection methods are worse than ‘oneshot’ methods. Any method that solves the problem
above by solving one LP, SOCP, or SDP problem is better than any method that uses a
oneparameter bisection. In other words, use a bisection method only if you cannot ﬁnd
a ‘oneshot’ method.
• Use the simplest solver needed to solve the problem. We consider an LP solver to be
simpler than an SOCP solver, which is considered simpler than an SDP solver. Thus, a
method that uses an LP solver is better than a method that uses an SOCP solver, which
in turn is better than a method that uses an SDP solver.
14 3.7 The illumination problem. In lecture 1 we encountered the function
f (p) = max  log aT p − log Ides 
i
i=1,...,n m where ai ∈ R , and Ides > 0 are given, and p ∈ Rm .
+
(a) Show that exp f is convex on {p  aT p > 0, i = 1, . . . , n }.
i
(b) Show that the constraint ‘no more than half of the total power is in any 10 lamps’ is convex
(i.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
 F.Borrelli
 The Aeneid

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