bv_cvxbook_extra_exercises

38 schur complements and lmi representation

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Unformatted text preview: use the following rules: • Bisection methods are worse than ‘one-shot’ methods. Any method that solves the problem above by solving one LP, SOCP, or SDP problem is better than any method that uses a one-parameter bisection. In other words, use a bisection method only if you cannot find a ‘one-shot’ 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.

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