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

Question

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 (7×35)

f is a vector (7×1)

b is the vector (7×1)

w is the vector of parameters needed for optimization (35×1)

Answer 1

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