n
nicefa.
Advanced Proof

Convergence Proof of the Steepest Descent Method

Students often conflate the convergence of the gradient f(xk)0 \nabla f(x_k) \to 0 with the convergence of the iterates xkx x_k \to x^* . While the former is guaranteed under mild conditions, the latter requires the stronger assumption of strong convexity to ensure the sequence does not wander along a flat plateau.
Institutional Reference: Fundamentals of Optimization
View Full Proof →