Numerical optimization
This section briefly introduces the different optimization algorithms that can be applied to minimize the loss function, with or without a penalty term. These algorithms are described in greater detail in the Summary of optimization techniques section in Appendix A, Basic Concepts.
First, let's define the least squares problem. The minimization of the loss function consists of nullifying the first order derivatives, which in turn generates a system of D equations (also known as gradient equations), D being the number of regression weights (parameters). The weights are iteratively computed by solving the system of equations using a numerical optimization algorithm.
Note
The definition of the least squares-based loss function is as follows:
The generation of gradient equations with a Jacobian J matrix (refer to the Jacobian and Hessian matrices section in Appendix A, Basic Concepts) after minimization of the loss function L is described as follows:
Iterative approximation...
