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4.7 函数极值点
4.7.1 一元函数的极小值点
4.7.2 多元函数的极小值点
2 2
2
【例 4.7.2-1】求 f ( x,
y)
= 100(
y − x ) + ( 1−
x)
的极小值点。它即是著名的 Rosenbrock's
"Banana" 测试函数。该测试函数有一片浅谷,许多算法难以越过此谷。(演示本例搜索过程
的文件名为 exm04072_1_1.m 。)
(1)
ff=inline('100*(x(2)-x(1)^2)^2+(1-x(1))^2','x');
(2)
x0=[-1.2,1];[sx,sfval,sexit,soutput]=fminsearch(ff,x0)
sx =
1.0000 1.0000
sfval =
8.1777e-010
sexit =
1
soutput =
iterations: 85
funcCount: 159
algorithm: 'Nelder-Mead simplex direct search'
(3)
[ux,sfval,uexit,uoutput,grid,hess]=fminunc(ff,x0)
Warning: Gradient must be provided for trust-region method;
using line-search method instead.
> In D:\MATLAB6P1\toolbox\optim\fminunc.m at line 211
Optimization terminated successfully:
Current search direction is a descent direction, and magnitude of
directional derivative in search direction less than 2*options.TolFun
ux =
1.0000 1.0000
sfval =
1.9116e-011
uexit =
1
uoutput =
iterations: 26
funcCount: 162
stepsize: 1.2992
firstorderopt: 5.0020e-004
algorithm: 'medium-scale: Quasi-Newton line search'
grid =
1.0e-003 *
-0.5002
-0.1888
hess =
820.4028 -409.5496
-409.5496 204.7720
4.8 数值积分
12