[袁亚湘]从瞎子爬山到最优化方法.pdfVIP

  Æ  ”, Æ ℄ ”, (1910-1985) Æ min f (x) (1) x∈ℜn x = x + α (−∇f (x )) , k+1 k k k αk 0 αk ℄ f (x) αk = α∗ ∗ f (x − α ∇f (x )) = min f (x − α∇f (x )) . k k k k α0  ℄ min f (x, y) = 100x2 + y2 (1, 100) Æ Steepest descent with exact line search 100 95 90 85 y 80 75 70 65 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 x + = 1988  Borwein Barzilai