MATLAB: I want to minimize l1-norm problem stated as argmin_v ||v^T*X||_1 such that ||v||_2=1 , X is a matrix having feature vector in each column? Does MATLAB optimization toolbox have function to do that

l1 norm minimization

I want to minimize l1-norm problem stated as argmin_v |v^T*X|_1 such that |v|_2=1 , X is a matrix having feature vector in each column? Does MATLAB optimization toolbox have function to do that?

Best Answer

Use fmincon to solve the problem
min: sum_{i=1}^{i=N} (z1_i+z2_i)
s.c.
y = z1 - z2 
v^T*X - y = 0
v^T*v = 1
z1, z2 >= 0
Best wishes
Torsten.
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