bv_cvxbook_extra_exercises

Bv_cvxbook_extra_exercises

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Unformatted text preview: g., a QP, SOCP, or SDP. You can introduce new variables if needed. Your reformulation should have a number of variables and constraints that grows linearly with m and n, and not exponentially. (b) Consider the specific problem instance with m = 4, n = 3, A= 60 ± 0.05 45 ± 0.05 −8 ± 0.05 90 ± 0.05 30 ± 0.05 −30 ± 0.05 0 ± 0.05 −8 ± 0.05 −4 ± 0.05 30 ± 0.05 10 ± 0.05 −10 ± 0.05 , b= −6 −3 18 −9 . ¯ (The first part of each entry in A gives Aij ; the second gives Rij , which are all 0.05 here.) Find ¯ the solution xls of the nominal problem (i.e., minimize Ax − b 2 ), and robust least-squares solution xrls . For each of these, find the nominal residual norm, and also the worst-case residual norm. Make sure the results make sense. 5.10 Identifying a sparse linear dynamical system. A linear dynamical system has the form x(t + 1) = Ax(t) + Bu(t) + w(t), t = 1, . . . , T − 1, where x(t) ∈ Rn is the state, u(t) ∈ Rm is the input signal, and w(t) ∈ Rn is the process noise, at time t. We assume the process noises are IID N (0, W...
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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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