Convex Function

Definitions are written by AI from each lecture’s transcript. The time opens the lecture where the lecturer explains it.

• A function whose epigraph is a convex set, satisfying $f(\alpha x + \beta y) \le \alpha f(x) + \beta f(y)$ for non-negative $\alpha, \beta$ summing to one.

  1:02:30Mathematical Optimization & Why Convexity Is the WatershedStephen Boyd · Stanford University
• A simpler cost function visualized as a parabolic shape where local minima are guaranteed to be global minima over a convex set.

  11:36Optimization: A Bootcamp for Machine Learning, Inverse Problems, and ControlSteve Brunton · University of Washington
• A function where the line segment connecting any two points on the function is greater than or equal to the function value.

  4:32Convexity 101Steve Brunton · University of Washington