bv_cvxbook_extra_exercises

# now we describe the cameras the object at location x

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Unformatted text preview: 1 (y (j ) ), f3 (y (j ) )}, j = 1, . . . , M, f3 (z (j ) ) > max{f1 (z (j ) ), f2 (z (j ) )}, j = 1, . . . , P. In words: f1 is the largest of the three functions on the x data points, f2 is the largest of the three functions on the y data points, f3 is the largest of the three functions on the z data points. We can give a simple geometric interpretation: The functions f1 , f2 , and f3 partition Rn into three regions, R1 = {z | f1 (z ) > max{f2 (z ), f3 (z )}}, R2 = {z | f2 (z ) > max{f1 (z ), f3 (z )}}, R3 = {z | f3 (z ) > max{f1 (z ), f2 (z )}}, 62 deﬁned by where each function is the largest of the three. Our goal is to ﬁnd functions with x(j ) ∈ R1 , y (j ) ∈ R2 , and z (j ) ∈ R3 . Pose this as a convex optimization problem. You may not use strict inequalities in your formulation. Solve the speciﬁc instance of the 3-way separation problem given in sep3way_data.m, with the columns of the matrices X, Y and Z giving the x(j ) , j = 1, . . . , N , y (j ) , j = 1, . . . , M and z (j ) , j = 1, . . . , P . To s...
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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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