How to simulate the given optimization problem related to SVM in MATLAB ?

Hello all, I am trying to optimize the following problem in MATLAB. It is related to multiclass classification using SVM. There are total 16 classes (𝓁 is from 1 to 16).

where is a column vector of dimension , is also a column vector of dimension , is matrix of dimension , is row vector of and is the Gaussian radial basis function, where is the variance.

The main moto in this optmization problem is to obtain the value of α for 16 different 𝓁 i.e., I have to obtain .

With the help from Torsten (Level 9 MVP) and Matt J (Level 10 MVP), I had understood how to solve the function inside two summation.

My query is for 16 different b each of dimension , how to solve this optimization problem.

Any help in this regard will be highly appreciated.

[charu shree]

I have the following code for .

K=rand(3);

K=K*K.';

b=rand(3,1)-0.5;

C=5;

alpha=optimvar('alpha',numel(b),'LowerBound',0,'UpperBound',C);

prob=optimproblem('Objective',alpha.'*(b.*K.*b')*alpha/2-sum(alpha),...

'Constraints', b'*alpha==0);

sol=solve(prob).alpha

So by repeating the above code 16 times, we get 16 different α i.e.,

So is this approach correct ?

[charu shree]

Any hint in this regard will be highly appreciated.

[Catalytic]

So is this approach correct ?

Probably. But why not just try it, rather than waiting hours and hours for other people to weight in? You could have verified by now whether it works.

[Torsten]

@charu shree

The code above is not for l=1, but a general code for arbitrary dimension of alpha.

You only need to fill in the correct values for K, b and C instead of the phantasy values used here:

K=rand(3); 
K=K*K.';
b=rand(3,1)-0.5;
C=5;