bv_cvxbook_extra_exercises

E is x equal to w does it include auxiliary variables

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Unformatted text preview: and S ≻ 0. • If A ≻ 0, then X 0 if and only if S 0. •X 0 if and only if A 0, B T (I − AA† ) = 0 and C − B T A† B 0, where A† is the T A† B serves as a generalization of the Schur complement in pseudo-inverse of A. (C − B the case where A is positive semidefinite but singular.) Prove one of these theorems. (You can choose which one.) 85 11 Circuit design 11.1 Interconnect sizing. In this problem we will size the interconnecting wires of the simple circuit shown below, with one voltage source driving three different capacitive loads Cload1 , Cload2 , and Cload3 . Cload1 Cload2 Cload3 We divide the wires into 6 segments of fixed length li ; our variables will be the widths wi of the segments. (The height of the wires is related to the particular IC technology process, and is fixed.) The total area used by the wires is, of course, w i li . A= i We’ll take the lengths to be one, for simplicity. The wire widths must be between a minimum and maximum allowable value...
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