bv_cvxbook_extra_exercises

n 2 for some vectors p1 pn of arbitrary dimension

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Unformatted text preview: n with rank n, with m ≥ n. We know y and A, but we don’t know v ; our goal is to estimate x. We make only one assumption about the measurement error v : v ∞ ≤ ǫ. We will estimate x using a linear estimator x = By ; we must choose the estimation matrix B ∈ ˆ Rn×m . The estimation error is e = x − x. We will choose B to minimize the maximum possible ˆ value of e ∞ , where the maximum is over all values of x and all values of v satisfying v ∞ ≤ ǫ. (a) Show how to find B via convex optimization. (b) Numerical example. Solve the problem instance given in minimax_fit_data.m. Display the x you obtain and report x − xtrue ∞ . Here xtrue is the value of x used to generate the ˆ ˆ measurement y ; it is given in the data file. 6.12 Cox proportional hazards model. Let T be a continuous random variable taking on values in R+ . We can think of T as modeling an event that takes place at some unknown future time, such as the death of a living person or a machine failure. The su...
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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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