Hello world;

I want to optimize my model based on two contraints. My goal is to find the W matrix that minimize this abs(W*x – Y). This can be done using gradient descent or some other models. In addition i want the model to be biased to some points of (x , y) based on a contraint that i will give. such as x*2 = y …. or something else, which is available just for some samples in the data.

Overall, i want that the model will be regularized by a second constraint that will keep it biased to some samples but not overfitted on under fitted on the other samples.

Which cost-function or optimization algorithm should i look for?