How to solve optimization problem using sequential minimal optimization (SMO) in MATLAB
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Hello all, I have the following optimization problem .
where 
is a column vector of dimension 
, 
is also a column vector of dimension and 
is matrix of dimension 
and 
is 
row vector of .
is a column vector of dimension , is also a column vector of dimension and is matrix of dimension and is row vector of .My query is How to solve it using sequential minimal optimization (SMO) in MATLAB ?
Any help in this regard will be highly appreciated.
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Matt J
2023-3-18
0 个投票
There is this offering on the File Exchange, which I have never used,
7 个评论
charu shree
2023-3-18
charu shree
2023-3-20
Torsten
2023-3-20
Here is the implementation of the constraints:
Aeq = b_l;
beq = zeros(size(b_l));
lb = zeros(size(b_l));
ub = C*ones(size(b_l));
charu shree
2023-3-20
You could also use the problem-based set-up, e.g.,
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
charu shree
2023-3-20
Thank you sir for your detailed answer.
Basically, 
is the Gaussian radial basis function.
is the Gaussian radial basis function. My query is that as both l, j in 
and
is from 1 to 
, hence the norm inside exponential will always be zero, then how should we tackle this inside the two summations ?
and is from 1 to , hence the norm inside exponential will always be zero, then how should we tackle this inside the two summations ?My query is that as both l, j in and is from 1 to L_t, hence the norm inside exponential will always be zero, then how should we tackle this inside the two summations ?
No, the norm will be non-zero whenever the vectors pr[l] and pr[j] are different. Also, this seems far afield now from your originally-posted question. Even if all the norms were zero, the ways to proceed with the optimization, which Torsten and I have already described, would not change.
If your original question has been answered, please Accept-click the answer and post any new questions you may have in a new thread.
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