Optimization Paths Across Directions with Different Curvature
f(w₁, w₂) = 0.5·w₁² + 10·w₂² | Start (-8.0, 4.0) → Minimum (0.0, 0.0)
Compare All Methods
3 methods
Compare curvature handling
Gradient Descent (GD)
30+ steps
Pronounced zigzag oscillation
Newton's Method
1 step
Exact curvature scaling
BFGS
2 steps
Estimate curvature from gradient changes
Algorithm:
GD
Step:
0
Coordinates (w₁, w₂):
(-8.00, 4.00)
Objective:
192.0000
Gradient Descent (GD, η=0.08)
Newton's Method (1 step)
BFGS (Exact line search)
View:
Compare all trajectories
Show GD oscillation only
Show Newton's one-step path
Show BFGS two-step convergence
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Animation speed / progress:
30 / 30