如何在“scipy.optimize.least_squares”中添加 Tikhonov 正则化？

Question

As the title, could anyone tell me a way to add "Tikhonov regularization" in "scipy.optimize.least_squares"? The default seems L2.

Answer 1

A straightforward way is to add more rows to your design matrix and objective vector.

In other words if you have A and b, and seek x to minimise

||A*x-b||

and you change A and b to

A~ = (A)
     (K)
b~ = (b)
     (k)

then the least squares problem: minimise

||A~*x - b~||

is minimising

||A*x-b||^2 + ||K*x-k||^2