The condition number of a function relative to a set

Understand

The condition number of a differentiable convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the function.

• In particular, the condition number of a quadratic convex function is the square of the aspect ratio of a canonical ellipsoid associated to the function.
• Furthermore, the condition number of a function bounds the linear rate of convergence of the gradient descent algorithm for unconstrained convex minimization.
• We propose a condition number of a differentiable convex function relative to a reference convex set and distance function pair.