How to solve the follow equation XX is the variable: A∘(XB)+CX=DA∘(XB)+CX=D
where A∘BA∘B is element-wise product or Hadamard product.
if the A=1n×nA=1n×n. the above equation becomes (XB)+CX=A(XB)+CX=A become Sylvester equation and can be solved. But how to solve with AA is any binary matrix.
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This is just solving a linear system of equations. Here is how it can be done in CVX and YALMIP. These are optimizers, but in this case, only a constraint is specified, and no objective is needed.
CVX
cvx_begin variable X(n,n) A.*(X*B) + C*X == D cvx_end disp(X)
YALMIP
X = sdpvar(n,n,'full') optimize(A.*(X*B) + C*X == D) disp(value(X))
CVX
cvx_begin variable X(n,n) A.*(X*B) + C*X == D cvx_end disp(X)
YALMIP
X = sdpvar(n,n,'full') optimize(A.*(X*B) + C*X == D) disp(value(X))
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