凸二次规划梯度类算法中步长对收敛速度的影响.pdf

1 1 1 2 1 3 4 , , , , , 1 , (210093) 2 , (210096) 3 , (213016) 4 , (200052) E-mail: hebma@ : , 1 . , 5 , [0.3, 0.99] , . . , , , . , , . : , , . 1 Ω Rn , c ∈ Rn , H ∈ Rn ×n , min 1xT Hx + cT x |x ∈ Ω (1.1) 2 x ∈ Ω, (x − x)T (Hx + c) ≥ 0, ∀x ∈ Ω. , [8–10,12,14] . PΩ (·) Ω , (1.1) e(x, β) = x − PΩ [x − β (Hx + c)] (1.2) , β . [9, 10] , , k+1 k ∗ k x = x − γ α e(x , β), (1.3) k k 1 ( : ( : 20060284001). 1 k 2 ∗ e(x , β) αk = k 2 k T k (1.4) e(x , β) + e(x , β) βHe(x , β) “”, γk ∈ (0, 2) . {xk } k+1 ∗ 2 k ∗ 2 ∗ k 2 x − x (I +βH ) ≤ x − x (I +βH ) − γk (2 − γk )αk e(x , β) . (1.5) [9, 10] (1.5) . e(xk , β)T βHe(xk , β) rk := k 2 , (1.6) e(x , β) (1.4) α∗ , k