iteratively reweighted least squares

The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems with objective functions of the form of a ''p''-norm: :

\underset  \sum_^n \big,  y_i - f_i (\boldsymbol\beta) \big, ^p,

by an iterative method in which each step involves solving a weighted least squares problem of the form:C. Sidney Burrus,
Iterative Reweighted Least Squares
' :

\boldsymbol\beta^ = \underset  \sum_^n w_i (\boldsymbol\beta^) \big,  y_i - f_i (\boldsymbol\beta) \big, ^2.

IRLS is used to find the maximum likelihood estimates of a

generalized linear model In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and b ...

, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set. For example, by minimizing the

least absolute errors Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based minimizing the ''sum o ...

rather than the least square errors. One of the advantages of IRLS over

linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, li ...

and convex programming is that it can be used with