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how to maximize the two-norm of one vector?

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Stanley Cheng
Stanley Cheng 2014-11-10
回答： Torsten 2014-11-10
Hi everyone,
I am trying to solve one equation: Ax=b
where A is a 4*3 non-rectangular matrix, x is the 3*1 unknown vector and b is the 3*1 vector.
I know if the minimum two norm sum of x, i.e. sqrt(x(1)^2+x(2)^2+x(3)^2), is wanted, then the solution is
x=pinv(A)*b, where pinv(A) is the pseudo-inverse matrix of A, that meets pinv(A)*A=A*pinv(A)=I, where I
is the identity matrix.
On the contrast, if the maximum two norm sum of x is wanted, how should I do it ?
Thanks very much !

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回答（2 个）

Stanley Cheng
Stanley Cheng 2014-11-10
Sorry A is a 2*3 non-rectangular matrix...
Torsten
Torsten 2014-11-10
Your problem is unbounded in x.
Thus it does not have a solution.
Best wishes
Torsten.

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