[微積]求兩題gradient分析?

[jolin19 (alex)]

(1)Run gradient descent, staring at (-0.8,-0.8)
with "alpha"=0.2 and 139 iterations, for the surface
z=f(x,y)=exp(x*y) / (exp(x^2*y^2) +1), -3<=x<=3, -3<=y<=3

Q1:Explain why the algorithm stalls and does not descend further?

(2)Run gradient "ascent", staring at (-0.6,-2.3)
with "alpha"=0.1 and 529 iterations, for the surface
z=f(x,y)=(y^2*x^(2/3))/x^2+y^2+1, -3<=x<=3, -3<=y<=3
Q2:Explain why the algorithm zig-zags around the optima?

只會用matlab跑出圖形,但不知道怎explain有無高手可幫忙!感恩!

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→ as7218      : (1) 因為已經走到local minumum, 所以不動了
→ as7218      : 至於 (2) 是不是有打錯？
sorry,(2)因該是ascent,f(x,y)=(y平方*x平方開三次方根)/(x平方+y平方+1)
再麻煩幫我解答
※ 編輯: jolin19 (151.181.36.98), 09/15/2017 23:05:44
→ as7218      : hmm..不過應該是descent才會有"zig-zags"的情況
→ as7218      : 你觀察 ∂f/∂x 的圖形，靠近 x=0 時的值會變大
→ as7218      : 這個時候走的步數較大時會跨過 x=0
→ as7218      : 所以就會在 x=0 兩邊跳來跳去