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Unformatted text preview: s criterion N ( f ( t k ) − yk ) 2 . k=1 We will use B-splines to parametrize f , so the variables in the problem are the coefficients x in f (t) = xT g (t). The problem can then be written as N minimize subject to x T g ( t k ) − yk k=1 x T g ( t) 2 (21) is convex in t on [α0 , αM ]. (a) Express problem (21) as a convex optimization problem of the form minimize Ax − b subject to Gx h. 2 2 (b) Use CVX to solve a specific instance of the optimization problem in part (a). As in the figures above, we take M = 10 and α0 = 0, α1 = 1, . . . , α10 = 10. Download the Matlab files spline_data.m and bsplines.m. The first m-file is used to generate the problem data. The command [t, y] = spline_data will generate two vectors t, y of length N = 51, with the data points tk , yk . The second function can be used to compute the B-splines, and their first and second derivatives, at any given point u ∈ [0, 10]. The command [g, gp, gpp] = bsplines(u) returns ′′ ′ three vectors of length 13 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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