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Unformatted text preview: (8).
31 (d) Solve the dual problem (9) using CVX. Generate problem instances using the Matlab code
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
(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.
- Fall '13
- The Aeneid