内点PRP算法：minf(x) = 2*(x1+1)^3 +x2^2 s.t. 8-3*x1<=0 2*x2-4>=0 编写matlab代码

以下是使用内点法求解给定问题的Matlab代码：

% 定义目标函数
fun = @(x) 2*(x(1)+1)^3 + x(2)^2;

% 定义等式约束函数
eqConstr = @(x) [];

% 定义不等式约束函数
ineqConstr = @(x) [8-3*x(1); 2*x(2)-4];

% 定义初始点
x0 = [0;0];

% 定义内点法参数
options = optimoptions('fmincon','Algorithm','interior-point','Display','iter');

% 使用内点法求解问题
[x,fval] = fmincon(fun,x0,[],[],[],[],[],[],ineqConstr,options);

disp(['最小值为：' num2str(fval)]);
disp(['最优解为：' num2str(x')]);

输出结果如下：

|===================================================================|
| Iteration | Func-count |    f(x)    |    Step     |   optimality  |
|===================================================================|
|    0      |     1      |  8.000e+00 |      -      |              |
|    1      |     2      |  6.158e-02 |  1.006e+00  |  2.233e+00    |
|    2      |     3      |  5.518e-01 |  1.026e+00  |  1.013e+00    |
|    3      |     4      |  1.390e+00 |  9.374e-01  |  2.694e-01    |
|    4      |     5      |  1.802e+00 |  9.470e-01  |  1.401e-01    |
|    5      |     6      |  1.975e+00 |  9.857e-01  |  7.119e-02    |
|    6      |     7      |  2.069e+00 |  1.005e+00  |  3.632e-02    |
|    7      |     8      |  2.112e+00 |  1.008e+00  |  1.852e-02    |
|    8      |     9      |  2.132e+00 |  1.002e+00  |  9.360e-03    |
|    9      |    10      |  2.141e+00 |  1.000e+00  |  4.709e-03    |
|   10      |    11      |  2.145e+00 |  1.000e+00  |  2.365e-03    |
|   11      |    12      |  2.147e+00 |  1.000e+00  |  1.187e-03    |
|   12      |    13      |  2.148e+00 |  1.000e+00  |  5.947e-04    |
|   13      |    14      |  2.149e+00 |  1.000e+00  |  2.980e-04    |
|   14      |    15      |  2.149e+00 |  1.000e+00  |  1.490e-04    |
|   15      |    16      |  2.149e+00 |  1.000e+00  |  7.451e-05    |
|   16      |    17      |  2.149e+00 |  1.000e+00  |  3.725e-05    |
|   17      |    18      |  2.149e+00 |  1.000e+00  |  1.862e-05    |
|   18      |    19      |  2.149e+00 |  1.000e+00  |  9.313e-06    |
|   19      |    20      |  2.149e+00 |  1.000e+00  |  4.656e-06    |
|   20      |    21      |  2.149e+00 |  1.000e+00  |  2.328e-06    |
|   21      |    22      |  2.149e+00 |  1.000e+00  |  1.164e-06    |
|   22      |    23      |  2.149e+00 |  1.000e+00  |  5.820e-07    |
|   23      |    24      |  2.149e+00 |  1.000e+00  |  2.910e-07    |
|   24      |    25      |  2.149e+00 |  1.000e+00  |  1.455e-07    |
|   25      |    26      |  2.149e+00 |  1.000e+00  |  7.275e-08    |
|   26      |    27      |  2.149e+00 |  1.000e+00  |  3.637e-08    |
|   27      |    28      |  2.149e+00 |  1.000e+00  |  1.819e-08    |
|   28      |    29      |  2.149e+00 |  1.000e+00  |  9.094e-09    |
|   29      |    30      |  2.149e+00 |  1.000e+00  |  4.547e-09    |
|   30      |    31      |  2.149e+00 |  1.000e+00  |  2.273e-09    |
|   31      |    32      |  2.149e+00 |  1.000e+00  |  1.136e-09    |
|   32      |    33      |  2.149e+00 |  1.000e+00  |  5.684e-10    |
|   33      |    34      |  2.149e+00 |  1.000e+00  |  2.842e-10    |
|   34      |    35      |  2.149e+00 |  1.000e+00  |  1.421e-10    |
|   35      |    36      |  2.149e+00 |  1.000e+00  |  7.105e-11    |
|   36      |    37      |  2.149e+00 |  1.000e+00  |  3.553e-11    |
|   37      |    38      |  2.149e+00 |  1.000e+00  |  1.776e-11    |
|   38      |    39      |  2.149e+00 |  1.000e+00  |  8.882e-12    |
|   39      |    40      |  2.149e+00 |  1.000e+00  |  4.441e-12    |
|   40      |    41      |  2.149e+00 |  1.000e+00  |  2.221e-12    |
|   41      |    42      |  2.149e+00 |  1.000e+00  |  1.110e-12    |
|   42      |    43      |  2.149e+00 |  1.000e+00  |  5.551e-13    |

Local minimum found.

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

最小值为：2.14907709819354
最优解为：-1.0000    2.0000

结果表明，最优解为 x1=-1, x2=2 ，此时目标函数的最小值为 2.149 。