Hello every one, I have a question related to approximation of functions based on norms

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Ahmed Galal 2020-11-14

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评论： Ahmed Galal 2020-11-16

How can I approximate this function and its constraint using L1, L2, and L∞ to perform the optimization process using fmincon MATLAB function?

Objective function F*w+f=min

Subject to F*w+f ≥b

F is a matrix (7x35)

f is a vector (7x1)

b is the vector (7x1)

w is the vector of parameters needed for optimization (35x1)

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Matt J 2020-11-14

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You would not use fmincon. For L1, you could use minl1lin

https://www.mathworks.com/matlabcentral/fileexchange/52795-constrained-minimum-l1-norm-solutions-of-linear-equations

For L2, you would use lsqlin,

https://www.mathworks.com/help/optim/ug/lsqlin.html

For L-infinity, you would use fminimax,

https://www.mathworks.com/help/optim/ug/fminimax.html

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Ahmed Galal 2020-11-14

编辑：Ahmed Galal 2020-11-14

Optimization model.jpg

What should I do if some constraints included in the norms like the attached example. Please find the attached example

The first constraint is L∞-NORM

The second constraint is L1-NORM

Matt J 2020-11-14

That's a much different question. You should post it in a separate thread.

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Bruno Luong 2020-11-14

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l1 and linfinity can be formulate as linear programming, so LINPROG is better.

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Matt J 2020-11-14

The first constraint in Ahmed's addendum is non-convex. It looks difficult to recast that as a linear program.

Ahmed Galal 2020-11-16

Thank you very much sir Bruno Luong for helping, also for your kind words.

Thanks also extending for sir Matt.

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