Outline
- basic properties and examples
- operations that preserve convexity
- the conjugate function
- quasiconvex functions
- log-concave and log-convex functions
- convexity with respect to generalized inequalities
1.Definition
f:\mathbb{R}^n\to\mathbb{R} is convex if \textbf{dom} f is a convex set and
f(\theta x+(1-\theta)y)\leq\theta f(x)+(1-\theta)f(y)
for all x,y\in\textbf{dom} f,0\leq\theta\leq 1
