非线性优化问题---超大对象函数优化问题---MATLAB

n = 200;
x0 = 10*ones(1,n); %初始迭代点
PTIONS = optimset('LargeScale','on','display','iter','TolFun',1e-8);
[x,fval,exitflag,output] = fminunc(@LargObjFun,x0,PTIONS)```

```clike
function f=LargObjFun(x)
f=0;
n = 200;
for ii=1:n
    f=f+(x(ii)-1/ii)^2;
end```

```handlebars
    First-order 
 Iteration  Func-count       f(x)        Step-size       optimality
     0         201          19884.1                            20
     1         402          16104.3       0.050025             18  
     2         603      6.31478e-07              1       0.000287  
     3         804      1.11396e-14              1        8.9e-10  

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

<stopping criteria details>

x =

  列 1 至 14

    1.0000    0.5000    0.3333    0.2500    0.2000    0.1667    0.1429    0.1250    0.1111    0.1000    0.0909    0.0833    0.0769    0.0714

  列 15 至 28

    0.0667    0.0625    0.0588    0.0556    0.0526    0.0500    0.0476    0.0455    0.0435    0.0417    0.0400    0.0385    0.0370    0.0357

  列 29 至 42

    0.0345    0.0333    0.0323    0.0312    0.0303    0.0294    0.0286    0.0278    0.0270    0.0263    0.0256    0.0250    0.0244    0.0238

  列 43 至 56

    0.0233    0.0227    0.0222    0.0217    0.0213    0.0208    0.0204    0.0200    0.0196    0.0192    0.0189    0.0185    0.0182    0.0179

  列 57 至 70

    0.0175    0.0172    0.0169    0.0167    0.0164    0.0161    0.0159    0.0156    0.0154    0.0152    0.0149    0.0147    0.0145    0.0143

  列 71 至 84

    0.0141    0.0139    0.0137    0.0135    0.0133    0.0132    0.0130    0.0128    0.0127    0.0125    0.0123    0.0122    0.0120    0.0119

  列 85 至 98

    0.0118    0.0116    0.0115    0.0114    0.0112    0.0111    0.0110    0.0109    0.0108    0.0106    0.0105    0.0104    0.0103    0.0102

  列 99 至 112

    0.0101    0.0100    0.0099    0.0098    0.0097    0.0096    0.0095    0.0094    0.0093    0.0093    0.0092    0.0091    0.0090    0.0089

  列 113 至 126

    0.0088    0.0088    0.0087    0.0086    0.0085    0.0085    0.0084    0.0083    0.0083    0.0082    0.0081    0.0081    0.0080    0.0079

  列 127 至 140

    0.0079    0.0078    0.0078    0.0077    0.0076    0.0076    0.0075    0.0075    0.0074    0.0074    0.0073    0.0072    0.0072    0.0071

  列 141 至 154

    0.0071    0.0070    0.0070    0.0069    0.0069    0.0068    0.0068    0.0068    0.0067    0.0067    0.0066    0.0066    0.0065    0.0065

  列 155 至 168

    0.0065    0.0064    0.0064    0.0063    0.0063    0.0062    0.0062    0.0062    0.0061    0.0061    0.0061    0.0060    0.0060    0.0060

  列 169 至 182

    0.0059    0.0059    0.0058    0.0058    0.0058    0.0057    0.0057    0.0057    0.0056    0.0056    0.0056    0.0056    0.0055    0.0055

  列 183 至 196

    0.0055    0.0054    0.0054    0.0054    0.0053    0.0053    0.0053    0.0053    0.0052    0.0052    0.0052    0.0052    0.0051    0.0051

  列 197 至 200

    0.0051    0.0051    0.0050    0.0050


fval =

   1.1140e-14


exitflag =

     1


output = 

  包含以下字段的 struct:

       iterations: 3
        funcCount: 804
         stepsize: 7.9471e-04
     lssteplength: 1
    firstorderopt: 8.8988e-10
        algorithm: 'quasi-newton'
          message: '↵Local minimum found.↵↵Optimization completed because the size of the gradient is less than↵the value of the optimality tolerance.↵↵<stopping criteria details>↵↵Optimization completed: The first-order optimality measure, 4.239518e-11, is less ↵than options.OptimalityTolerance = 1.000000e-08.↵↵'