bv_cvxbook_extra_exercises

E m i1 m z e 1 note that this can be considered

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Unformatted text preview: k) , k = 1, . . . , N , to be exactly solvable. To estimate the point x we therefore minimize the maximum error in the N equations by solving minimize g (x) = max fk (x) − y (k) 2 . (28) k=1,...,N (a) Show that (28) is a quasiconvex optimization problem. The variable in the problem is x ∈ R3 . The functions fk (i.e., the parameters Ak , bk , ck , dk ) and the vectors y (k) are given. (b) Solve the following instance of (28) using CVX (and bisection): N = 4, 1000 P1 = 0 1 0 0 , 0010 1 1 1 −10 11 0 , P3 = −1 −1 −1 1 10 y (1) = 0.98 0.93 , y (2) = 1.01 1.01 , 1 00 0 0 1 0 , P2 = 0 0 −1 0 10 0 11 0 P4 = 0 −1 1 0 , −1 0 0 10 y (3) = 0.95 1.05 , y (4) = 2.04 0.00 . You can terminate the bisection when a point is found with accuracy g (x) − p⋆ ≤ 10−4 , where p⋆ is the optimal value of (28). 7.10 Projection onto the probability simplex. In this problem you will work out a simple method for finding the Euclidean projection y of x ∈ Rn onto the probability simplex P = {z |...
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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 Berkeley.

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