bv_cvxbook_extra_exercises

612 cox proportional hazards model let t be a

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Unformatted text preview: urements m = 30; % total number of measurements to be carried out randn(’state’, 0); V=randn(n,p); % columns are vi, the possible measurement vectors 55 Solve the relaxed A-optimal experiment design problem, minimize (1/m) tr subject to 1T λ = 1, −1 p T i=1 λi vi vi λ 0, with variable λ ∈ Rp . Find the optimal point λ⋆ and the associated optimal value of the relaxed problem. This optimal value is a lower bound on the optimal value of the discrete A-optimal experiment design problem, −1 p T minimize tr i=1 mi vi vi subject to m1 + · · · + mp = m, mi ∈ {0, . . . , m}, i = 1, . . . , p, with variables m1 , . . . , mp . To get a suboptimal point for this discrete problem, round the entries in mλ⋆ to obtain integers mi . If needed, adjust these by hand or some other method to ensure that ˆ they sum to m, and compute the objective value obtained. This is, of course, an upper bound on the optimal value of the discrete problem. Give the gap between this upper bound and the lower bound obtained from the relaxed problem. Note t...
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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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