Solving for scalar in matrix norm minimization
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Is it possible in MATLAB to minimize argmin_alpha norm( X - alpha * Y , 1) (where X and Y are matrices)?
I want the following constraints:
alpha > 0, X - alpha * Y >= eps
Thanks
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Matt J
on 4 Sep 2014
The thing you propose to minimize X - alpha * Y _1 is not a scalar. Do you mean you want to minimize some squared norm of this difference? If so, which norm? L2? Frobenius?
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More Answers (1)
Matt J
on 4 Sep 2014
Edited: Matt J
on 4 Sep 2014
The system of linear inequalities
X(i) - alpha * Y(i) >= eps
are equivalent to some 1D interval [alpha_lower, alpha_upper]. Once you find this interval, you can apply fminbnd.
The analysis needed to find the interval is simple, but you could let this FEX file do it for you,
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