Prox is not working. X(:, i+1) is not well defined. When I put X = rand(10,1) and prox_L1(X, 0.5) then it's working. But I am not getting X(:, i+1). I want to run the followin

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feeroz babu
feeroz babu 2022-1-25
回答： Sriram Tadavarty 2023-6-8
n = 10;
p=1;
A= rand(n);
A= 0.5*(A'+ A);
i=1;
X(:,i)=rand(n,p);
lambd3(i) = 1/3;
mu = 0.9;
for i = 1:100
a_i = 1/(i+1)^0.5;
L=(norm(A))^2;
beta= abs(min(eig(A)));
s_i=2*beta/L;
gamma_i = 0.005*s_i;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
%%Alg1
f_i = -2*X(:,i)'*A'*A;
%2*A'*A*X(:,:,i) - 2*A'*B;
Z_i = X(:,i) - s_i*(f_i);
Y_i = prox_L1(Z_i,gamma_i);
X(:,i+1) = Y_i;
L(i) = norm(X(:,i+1) - X(:,i))
% n(i)=i;
end
n=[1:1:100];
plot(n,L(n),'color',[0.80 0 0], Marker='-.','LineWidth',2,'markersize',4);

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Sriram Tadavarty
Sriram Tadavarty 2023-6-8
Hi Feeroz,
Here are some of the inputs that I can provide without knowing how the prox_L1 code is.
The issue is that Z_i is a matrix of size 10 x 10, and this matrix is trying to fit to a vector X of size 10 x 1.
When the value of X(:,i) set to rand(n,p) gives a column vector of length 10, since p is 1. The matrix A is of size 10 x 10.
f_i = -2*X(:,i)'*A'*A; % Here f_i is of size 1 x 10
Z_i = X(:,i) - s_i*(f_i); % Here Z_i is of size 10 x 10
% This Z_i is passed to prox_L1 function, which might return the output
% with same dimensions thereby not able map to a vector of length 10.
When Z_i is of size 10 x 1, then the code would run as expected. So, updating f_i or Z_i could be a solution to avoid the issue.
Another aspect is to define X with zeros before accessing the elements, as it would make the code clear. Like, in this case X can be initialized to zeros(10,101). first input 10 is for n, second input 101 is to access all the i & i+1 values in the for loop.
Hope this helps.
Regards,
Sriram

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