How would you show that if you do logistic regression with a squared loss function, it is not a convex optimization problem (in parameters)?
In other words, your loss function for an individual observation is $(y - p)^2$, where $y$ is the dependent variable and $p$ is your prediction, and$$p = \frac{1}{1+\exp(-w^Tx)},$$where $x$ is the vector of predictors and $w$ is the vector of weights.
