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Unformatted text preview: ith elements gk (u), gk (u), and gk (u). (The right derivatives are
returned for u = 0, and the left derivatives for u = 10.)
Solve the convex spline ﬁtting problem (21) for this example, and plot the optimal spline.
45 5.9 Robust leastsquares with interval coeﬃcient matrix. An interval matrix in Rm×n is a matrix whose
entries are intervals:
¯
A = {A ∈ Rm×n  Aij − Aij  ≤ Rij , i = 1, . . . , m, j = 1, . . . , n}.
¯
The matrix A ∈ Rm×n is called the nominal value or center value, and R ∈ Rm×n , which is
elementwise nonnegative, is called the radius.
The robust leastsquares problem, with interval matrix, is
minimize supA∈A Ax − b 2 ,
¯
with optimization variable x ∈ Rn . The problem data are A (i.e., A and R) and b ∈ Rm . The
objective, as a function of x, is called the worstcase residual norm. The robust leastsquares
problem is evidently a convex optimization problem.
(a) Formulate the interval matrix robust leastsquares problem as a standard optimization problem, e....
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 Fall '13
 F.Borrelli
 The Aeneid

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