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V
G k
k ∈ {1, . . . , K} x k (t) ∈ R n w k (t) ∈ R n
lim
t→∞ xk (t) = x k ∗, lim w
t→∞ k (t) = w k ∗,
t → ∞ x k ∗ w k ∗ e k xw(t) =
[(x k (t)) T , (w k (t)) T ] T −[(x k ∗) T , (w k ∗) T ] T k ∈ {1, . . . , K} t
t
e k xw(t) ∞ ≤ e k xw(t) 2 ≤ αfk(t) + σgk(t),
fk(t) = β k λ t+(k−1)l
⋆ , gk(t) = βλ t k−2
⋆ (βλ l ⋆) p ,
l
β = 2 √ 10/3 λ⋆ α σ
x k (t) ∈ R n w k (t) ∈ R n x k ∗ w k ∗
l
p=0
k
exw(l) ≤ βλ 2 l
k
⋆ exw(0) .
2
ek xw(l) k ek+1 xw (0)
k + 1
e k+1
xw (0) = e k xw(l) +
x k ∗
w k ∗
−
x k+1
∗
w k+1
∗
k
exw(t) ≤ β 2 k λ t+(k−1)l
1
⋆ exw(0)
2
+ βλ t k−2
⋆ (βλ l ⋆) p
k−p−1
x∗
p=0
w k−p−1
∗
− x k−p
∗
− w k−p
∗
.
2
,
k = 1
k = 1 t = 0 e1 xw(0) = [(−x1 ∗) T , (−w1 ∗) T ] T
e1 xw(0)2 α
T T T (a , b ) 2 = a2
2 2 + b2 2
k = 1, . . . , K − 1 k ((x∗ − xk+1 ∗ ) T , (wk ∗ − wk+1 ∗ ) T ) T σk
2
σ