Convex Optimization: Algorithms & Complexity Visual Lab

Loss Landscape 2D & Trajectories

Gradient Descent Nesterov Accel. Polyak Heavy-Ball Newton's Method

Objective Preset

Condition κ (25)

Step Size η (0.040)

Max Steps K (50)

💡 Drag the black reticle (x₀) anywhere on the map to recompute convergence instantly. x₀ = (-3.50, 3.00)

Log Suboptimality: log₁₀(f(x_k) - f*) vs Oracle Bounds

Status: Verified

Algorithm	Final f(x_K)-f*	\|\|∇f(x_K)\|\|	Oracle Calls	Observed Rate

Bubeck Theorem Summary (Ch. 3 & 4):

Standard GD: Sublinear $O(1/k)$ on $L$-smooth convex; linear $O((1 - 1/\kappa)^k)$ on $\mu$-strongly convex.
Nesterov Accelerated: Optimal minimax rate $O(1/k^2)$ (smooth) and accelerated linear $O((1 - 1/\sqrt{\kappa})^k)$.
Newton's Method: Quadratic local convergence $O(e^{-2^k})$ with 2nd-order Hessian oracle.