# What are some reasons iteratively reweighted least squares would not converge when used for logistic regression?

I’ve been using the glm.fit function in R to fit parameters to a logistic regression model. By default, glm.fit uses iteratively reweighted least squares to fit the parameters. What are some reasons this algorithm would fail to converge, when used for logistic regression?

To clarify using mathematical notation, the heaviside function is $$lim\lim_{|\mathbf{w}| \rightarrow \infty}\sigma(\mathbf{w}^T x + b)$$, the limit of sigmoid function, where $$\sigma\sigma$$ is the sigmoid function and $$(\mathbf{w}, b)(\mathbf{w}, b)$$ determines the hyperplane solution. So IRLS theoretically does not stop and goes toward a $$\mathbf{w}\mathbf{w}$$ with increasing magnitude but would break in practice due to numerical problems.