How models actually learn, from vanilla gradient descent to Adam
A convex loss has a powerful guarantee: every local minimum is global. That makes optimization conceptually clean. Many classical ML objectives are convex; deep networks usually are not.
Convexity is still worth learning because it gives the reference case. It tells you what optimization would look like if there were no bad local traps, no saddle complications, and no severe landscape surprises.
A satellite dish has one clean aiming direction when the signal surface is smooth and single-peaked. Crumpled foil has many tiny shiny facets that can catch light locally. Convex optimization is closer to the dish; deep-network training is closer to the foil. The figure below shows the defining test on a convex curve: slide the two endpoints and notice that the straight chord between them never dips below the curve.