bv_cvxbook_extra_exercises

M give the values of a and b that you nd and verify

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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 least-squares 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 least-squares 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 worst-case residual norm. The robust least-squares problem is evidently a convex optimization problem. (a) Formulate the interval matrix robust least-squares problem as a standard optimization problem, e....
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