38 schur complements and lmi representation

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online