Matlab线性/非线性规划优化算法（5）

值得单独一说的是fminunc, fminseach, fminbnd的区别：
fminunc只能用于求解连续函数，对于变量没有限制
fminbnd只能用于求解单变量函数，
fminsearch只能用于求解多变量函数，

%%
clc
clear all
fun = @(x) -abs(1/x);
x0 = 1;
x1= -3;
x2 = 3;

我们解这个函数的最值，在0出可以取到最值，但函数在0处没有导数：

[x,fval,exitflag,output] = fminbnd(fun,x1,x2)
[x,fval,exitflag,output] = fminsearch(fun,x0)
[x,fval,exitflag,output] = fminunc(fun,x0)

求解这个函数，可以看到结果：

x =

   8.8818e-16


fval =

  -1.1259e+15


exitflag =

     1


output = 

  struct with fields:

    iterations: 17
     funcCount: 18
     algorithm: 'golden section search, parabolic interpolation'
       message: 'Optimization terminated:↵ the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04 ↵'

 
Exiting: Maximum number of function evaluations has been exceeded
         - increase MaxFunEvals option.
         Current function value: -1267650600228229401496703205376.000000 


x =

   7.8886e-31


fval =

  -1.2677e+30


exitflag =

     0


output = 

  struct with fields:

    iterations: 100
     funcCount: 200
     algorithm: 'Nelder-Mead simplex direct search'
       message: 'Exiting: Maximum number of function evaluations has been exceeded↵         - increase MaxFunEvals option.↵         Current function value: -1267650600228229401496703205376.000000 ↵'


Solver stopped prematurely.

fminunc stopped because it exceeded the function evaluation limit,
options.MaxFunctionEvaluations = 1.000000e+02.


x =

   2.2204e-16


fval =

  -4.5036e+15


exitflag =

     0


output = 

  struct with fields:

       iterations: 1
        funcCount: 101
         stepsize: 1.0000
     lssteplength: 1.0000
    firstorderopt: 3.0223e+23
        algorithm: 'quasi-newton'
          message: '↵Solver stopped prematurely.↵↵fminunc stopped because it exceeded the function evaluation limit,↵options.MaxFunctionEvaluations = 1.000000e+02.↵↵'

只有fminbnd的exitflag是1， 其他两个都是0， 因为这是一个单变量函数，所以fminsearch不能使用，又因为在0出不可导，所以fminunc也不能使用。