Convex (and non-convex) Optimization

Convex optimization is one of the keys to data science, both because some problems straight-up call for optimization solutions and because popular algorithms like a gradient descent solution to ordinary least squares are supported by optimization techniques. But there are all kinds of subtleties, starting with convex and non-convex functions, why gradient descent is really an optimization problem, and what that means for your average data scientist or statistician.