# Solving for scalar in matrix norm minimization

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matlab user guy on 4 Sep 2014
Commented: matlab user guy on 4 Sep 2014
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
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?
matlab user guy on 4 Sep 2014
Sorry there was a problem with the text. This should be the matrix norm. The double bars were removed.

Matt J on 4 Sep 2014
Edited: Matt J on 4 Sep 2014
If you have the Optimization Toolbox, you could also use fminimax, although that might be overkill for a simple scalar problem. Recall that the L1-norm of a matrix is its maximum absolute row sum.
matlab user guy on 4 Sep 2014
Thank you.
I have that toolbox. fminbnd doesn't seem to be working, but I'll check out fminimax.

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,