bv_cvxbook_extra_exercises

B construct a dual feasible point by applying the

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Unformatted text preview: (8). 31 (d) Solve the dual problem (9) using CVX. Generate problem instances using the Matlab code randn(’state’,0) m = 50; n = 40; A = randn(m,n); xhat = sign(randn(n,1)); b = A*xhat + s*randn(m,1); for four values of the noise level s: s = 0.5, s = 1, s = 2, s = 3. For each problem instance, compute suboptimal feasible solutions x using the the following heuristics and compare the results. (i) x(a) = sign(xls ) where xls is the solution of the least-squares problem Ax − b 2 . 2 minimize (ii) x(b) = sign(z ) where z is the optimal value of the variable z in the SDP (9). (iii) x(c) is computed from a rank-one approximation of the optimal solution of (9), as explained in part (b) above. (iv) x(d) is computed by rounding 100 samples of N (z, Z − zz T ), as explained in part (c) above. 4.11 Monotone transformation of the objective. Consider the optimization problem minimize f0 (x) subject to fi (x) ≤ 0, i = 1, . . . , m. (11) where fi : Rn → R for i = 0, 1, . . . , m are convex. Suppose φ...
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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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