bv_cvxbook_extra_exercises

As stopping criterion you can use 2 2 106 experiment

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Unformatted text preview: αt tr(∇f0 (X )∆X ) is satisfied. To check that a matrix X + t∆X is positive definite, you can use the Cholesky factorization with two output arguments ([R, p] = chol(A) returns p > 0 if A is not positive definite). Test your code on randomly generated problems of sizes n = 10, . . . , 100 (for example, using n = 100; C = randn(n); C = C + C’). 8.9 Estimation of a vector from one-bit measurements. A system of m sensors is used to estimate an unknown parameter x ∈ Rn . Each sensor makes a noisy measurement of some linear combination of the unknown parameters, and quantizes the measured value to one bit: it returns +1 if the measured value exceeds a certain threshold, and −1 otherwise. In other words, the output of sensor i is given by 1 a T x + v i ≥ bi i yi = sign(aT x + vi − bi ) = i − 1 a T x + v i < bi , i where ai and bi are known, and vi is measurement error. We assume that the measurement errors vi are independent random variables with a zero-mean unit-variance Gaussian distribution (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 University of California, Berkeley.

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