Why is convex optimization easier to solve?

• A. A function that is always non-convex.
• B. A function where the line segment between any two points lies above the graph; has a single global minimum.
• C. A function that is always increasing.
• D. A function defined only on a circular domain.

Answer: (B)

Convex optimization is easier because convexity guarantees that any local minimum is a global minimum. Geometrically, a convex function has the line segment between any two points on its graph lying above or on the graph, which means the surface cannot have isolated valleys or tricky traps. With this shape, descending from any starting point moves you toward the same best region, so there aren’t deceptive local minima to mislead the search. This makes the problem well-behaved and amenable to provable, efficient algorithms that converge to the global optimum, especially when the feasible set is also convex. The other descriptions don’t capture this crucial property: they describe traits that don’t guarantee a globally optimal solution or easy computational behavior.