11 数值优化方法.pdfVIP

Lecture 11: êêê???```zzz???{{{ ü?2 Monday 23rd November, 2009 Contents 1 Numerical optimization methods in R 1 1.1 Root-?nding in one dimension . . . . . . . . . . . . . . . . . 1 1.1.1 Bisection method . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Brent’s method . . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Newton’s method . . . . . . . . . . . . . . . . . . . . 8 1.1.4 Fisher scoring . . . . . . . . . . . . . . . . . . . . . . 17 1.2 multivariate optimization . . . . . . . . . . . . . . . . . . . 18 1.2.1 Newton’s method and Fisher scoring . . . . . . . . . 19 1.3 Numerical Integration . . . . . . . . . . . . . . . . . . . . . 20 1.4 Maximum Likelihood Problems . . . . . . . . . . . . . . . . 27 1.5 Optimization Problems . . . . . . . . . . . . . . . . . . . . . 29 1.5.1 One-dimension Optimization . . . . . . . . . . . . . 29 1.5.2 multi-dimensional Optimization . . . . . . . . . . . . 34 1.6 Linear Programming . . . . . . . . . . . . . . . . . . . . . . 38 Previous Next First Last Back Forward 1 Chapter 1 Numerical optimization methods in R 1.1 Root-?nding in one dimension bf : R → R???Y?ê, K?§f(x) = c?x, ÷vg(x) = f(x) ? c = 0. ?d·? ???f(x) = 0/a?§|?ˉK. |^ê??{|d ?§?, ?±àJ′|^f?ê?′ ?|^ê?{. New- ton? { ? ?Newton-Raphson? { ′ | ^ ?   ê  ? {, Brent ? z ?{1′?|^ê??|??{. 3R￥, ?êunirootò′? uBrent|??{. T?{Fortran §S “è?±3e??té /software/gsl/. 1R. Brent. Algorithms for minimization without derivatives. Prentice-Hall, New Jersey, 1973 Previous Next First Last Back Forward 1 1.1.1 Bisection method XJf(x)3?m[a, b]t?Y, ±9f(a)úf(b)k???ò, Kd￥??n?  ?3a c b, |f(c) = 0.