I am a newbie in the optimization domain. I am trying to solve a real-life problem. Where I have a set of equations to solve, with multiple variables.
The main equation looks like $x1[(w1*w7)+(w4*w8)]+x2[(w2*w7)+(w5*w8)]+x3[(w3*w7)+(w6*w8)] = y$
Here, x1, x2, x3, and y are known entities. I have around 500 equations having the same characteristics. Hence, I reduced them and got the below mentioned form.
${(w1*w7)+(w4*w8)=k1}$
${(w2*w7)+(w5*w8)=k2}$
${(w3*w7)+(w6*w8)=k3}$
Here, I only know the values of k1, k2, and k3. I know this problem has a non-convex characteristic but, is there a way to identify the values of w1, w2, w3, w4, w5, w6, w7, and w8.
Moreover, I can see the above set of equations as matrix form (AX=B) too.
Where, A could \begin{bmatrix} w1 & w4 \\ w2 & w5 \\ w3 & w6 \end{bmatrix} X \begin{bmatrix} w7 \\ w8 \\ \end{bmatrix}
B \begin{bmatrix} k1 \\ k2 \\ k3 \end{bmatrix}
Where I know B only.
I tried to initialize random values to matrix A to solve X. Unfortunately, I could not able to make an adaptation mechanism which updates the values of matrix A and leads to local minima.
I look forward to seeing the positive reply from the community.