Solving for scalar in matrix norm minimization

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matlab user guy 2014-9-4

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https://ww2.mathworks.cn/matlabcentral/answers/153460-solving-for-scalar-in-matrix-norm-minimization

评论： matlab user guy 2014-9-4

采纳的回答： Matt J

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 2014-9-4

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 2014-9-4

Sorry there was a problem with the text. This should be the matrix norm. The double bars were removed.

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Answer 1

Matt J 2014-9-4

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编辑：Matt J 2014-9-4

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.