Chapter 12: Optimization Methods. In the chapter mind map this icon labels Convex Sets & Functions. The discussion below is excerpted and lightly edited from § Example: Strictly Convex Functions in Mathematics for AI and Machine Learning.

• $f(x)=\log(1+e^{-x})$ (logistic loss; binary classification)
• $f(x)=x^2$ (squared loss; regression, L2 regularization)
• $f(x)=-\log x$ for $x>0$ (negative log-likelihood, MLE)

The top row of the book figure plots these three functions: each is strictly convex on its domain (the Hessian test below confirms $\nabla^2 f \succeq 0$), and they appear throughout supervised learning (classification, regression) and maximum-likelihood estimation.