bv_cvxbook_extra_exercises

Bv_cvxbook_extra_exercises

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online