用Octave计算二次规划问题
\(\frac{1}{2} x'×c×x+d'×x\)
\(
s.t. \quad
x ≥ 0
\)
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例子:
\(
\min \quad \frac{1}{2}
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}'
×
\begin{bmatrix}
1 & 2 \\
2 & 3
\end{bmatrix}
×
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
+
\begin{bmatrix}
4 \\ -5
\end{bmatrix}'
×
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
\)
定义矩阵 c,代码如下:
>> c = [1 2;
2 3];
定义矩阵 d,代码如下:
>> d = [4; -5];
求解,代码如下:
>> [x, minval, exitflag, output, lambda] = pqpnonneg (c, d)
x =
0
1.6667
minval = -4.1667
exitflag = 3
output =
scalar structure containing the fields:
algorithm = nnls-pqp
iterations = 3
lambda =
-7.3333
0