bv_cvxbook_extra_exercises

Here however the cost vector c is random normally

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Unformatted text preview: re A ∈ Cm×n , b ∈ Cm , and the variable is x ∈ Cn . Here defined as p = i=1 for p ≥ 1, and x ∞ p denotes the ℓp -norm on Cn , 1/p n x · | xi | p = maxi=1,...,n |xi |. We assume A is full rank, and m < n. (a) Formulate the complex least ℓ2 -norm problem as a least ℓ2 -norm problem with real problem data and variable. Hint. Use z = (ℜx, ℑx) ∈ R2n as the variable. (b) Formulate the complex least ℓ∞ -norm problem as an SOCP. (c) Solve a random instance of both problems with m = 30 and n = 100. To generate the matrix A, you can use the Matlab command A = randn(m,n) + i*randn(m,n). Similarly, use b = randn(m,1) + i*randn(m,1) to generate the vector b. Use the Matlab command scatter to plot the optimal solutions of the two problems on the complex plane, and comment (briefly) on what you observe. You can solve the problems using the CVX functions norm(x,2) and norm(x,inf), which are overloaded to handle complex arguments. To utilize this feature, you will need to declare variables to be com...
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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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