I am reading this topic of boyd book from convex optimization, but the following division i-e trade-off least square and l2 norm are difficult to understand for me. If kindly someone can explain equation, that how it has been calculated. Your guidance will be appreciated. Regards,
On
The solution to this "multi-objective" task is known to be $A^\dagger \,b$ with the Moore-Penrose pseudoinverse $A^\dagger$. If $A$ is injective, we have $$A^\dagger b = (A^* A)^{-1} A^* b.$$
In case $A$ is surjective, we have $$A^\dagger b = A^* (A\, A^*)^{-1} b$$
In the general case, one may apply Tikhonov regularization:
$$A^\dagger \,b = \lim_{\lambda \searrow 0} (A^*A + \lambda)^{-1} A^\intercal b = \lim_{\lambda \searrow 0} A^* (A\, A^* + \lambda)^{-1} b.$$
See also here.
My apologies, please ignore my question. I have solved my problem. I am just posting the answer in case someone needed. In case the question is too irrelevant here, it can be deleted. Regards