求解二次规划问题的最优解miny=11787-27.7x1-77.5x5-172.8x3^2+0.1x5^2+3.7x2x4+0.1x1x5-3.1x4x5+482.4x3x4,其中33≤x1≤200,33≤x2≤200,0.5≤x3≤5,0.3≤x4≤2.1,250≤x5≤400，matlab代码

可以使用MATLAB中的quadprog函数求解二次规划问题。首先将目标函数和约束条件转化为矩阵形式，然后调用quadprog函数求解即可。

代码如下：

% 目标函数系数矩阵
H = [0 -0.1 0 -3.7 -0.1; -0.1 0 0 0 0; 0 0 2*172.8 482.4 0; -3.7 0 482.4 0 3.1; -0.1 0 0 3.1 0];

% 目标函数常数项
f = [11787; 0; 0; 0; 0];

% 不等式约束系数矩阵
A = [1 0 0 0 0; 0 1 0 0 0; 0 0 1 0 0; 0 0 0 1 0; 0 0 0 0 1; -1 0 0 0 0; 0 -1 0 0 0; 0 0 -1 0 0; 0 0 0 -1 0; 0 0 0 0 -1];

% 不等式约束常数项
b = [200; 200; 5; 2.1; 400; -33; -33; -0.5; -0.3; -250];

% 调用quadprog函数求解
[x, miny] = quadprog(H,f,A,b,[],[],[33;33;0.5;0.3;250],[200;200;5;2.1;400]);

其中x为最优解，miny为目标函数的最小值。

相关问题

求解二次规划问题的最优解miny=11787-27.7x1-77.5x5-172.8x3^2+0.1x5^2+3.7x2x4+0.1x1x5-3.1x4x5+482.4x3x4,matlab代码

可以使用MATLAB中的quadprog函数求解二次规划问题的最优解。具体步骤如下：

1. 定义二次规划问题的目标函数、约束条件和变量范围。

H = [345.6, 0, 0, -345.6, 482.4; 
     0, 0, 3.7, 0, 0; 
     0, 3.7, -345.6, 0, 0; 
     -345.6, 0, 0, 691.2, -3.1; 
     482.4, 0, 0, -3.1, 0.2];
f = [-27.7; 0; 0; 0; 0];
A = [0, 0, 1, 0, 0; 
     1, 0, 0, 0, 0; 
     0, 0, 0, 0, 1];
b = [0; -11787; 0];
lb = [-inf; -inf; -inf; -inf; -inf];
ub = [inf; inf; inf; inf; inf];

其中，H是二次项系数矩阵，f是一次项系数矩阵，A和b是不等式约束条件，lb和ub是变量范围。

2. 调用quadprog函数求解最优解。

[x, y, exitflag] = quadprog(H, f, A, b, [], [], lb, ub);

其中，x是最优解向量，y是拉格朗日乘子向量，exitflag是求解状态。

3. 输出最优解。

miny = f' * x;
fprintf('The minimum value of the objective function is %f.\n', miny);
fprintf('The optimal solution is x1 = %f, x2 = %f, x3 = %f, x4 = %f, x5 = %f.\n', x(1), x(2), x(3), x(4), x(5));

完整的MATLAB代码如下：

H = [345.6, 0, 0, -345.6, 482.4; 
     0, 0, 3.7, 0, 0; 
     0, 3.7, -345.6, 0, 0; 
     -345.6, 0, 0, 691.2, -3.1; 
     482.4, 0, 0, -3.1, 0.2];
f = [-27.7; 0; 0; 0; 0];
A = [0, 0, 1, 0, 0; 
     1, 0, 0, 0, 0; 
     0, 0, 0, 0, 1];
b = [0; -11787; 0];
lb = [-inf; -inf; -inf; -inf; -inf];
ub = [inf; inf; inf; inf; inf];
[x, y, exitflag] = quadprog(H, f, A, b, [], [], lb, ub);
miny = f' * x;
fprintf('The minimum value of the objective function is %f.\n', miny);
fprintf('The optimal solution is x1 = %f, x2 = %f, x3 = %f, x4 = %f, x5 = %f.\n', x(1), x(2), x(3), x(4), x(5));

QCPAxis *yAxis = ui->customPlot->yAxis; double minY = std::numeric_limits<double>::max(); double maxY = std::numeric_limits<double>::min(); for (int i = 0; i < ui->customPlot->graphCount(); i++) { QCPGraph *graph = ui->customPlot->graph(i); if (graph->dataCount() == 0) { continue; } QCPGraphDataContainer::const_iterator it = graph->data().constBegin(); for (; it != graph->data().constEnd(); ++it) { double value = it->value; if (value < minY) { minY = value; } if (value > maxY) { maxY = value; } } } double range = qMax(qAbs(minY), qAbs(maxY)) * 2; double center = (minY + maxY) / 2; yAxis->setRange(center - range, center + range); 多条y轴，不是所有曲线共用y轴

如果多条曲线不是共用一个y轴，那么你需要对每个y轴分别进行自适应范围的计算和设置。

具体步骤如下：

1. 获取所有y轴的指针，可以通过QCustomPlot::axisRect()的成员函数axis()来获取。

QList<QCPAxis*> yAxisList;
for (int i = 0; i < ui->customPlot->axisRectCount(); i++) {
    QCPAxisRect *axisRect = ui->customPlot->axisRect(i);
    QCPAxis *yAxis = axisRect->axis(QCPAxis::atLeft);
    if (yAxis != nullptr) {
        yAxisList.append(yAxis);
    }
}

2. 遍历每个y轴对应的曲线，获取最小值和最大值。

double minY = std::numeric_limits<double>::max();
double maxY = std::numeric_limits<double>::min();
for (int i = 0; i < yAxisList.length(); i++) {
    QCPAxis *yAxis = yAxisList[i];
    minY = std::numeric_limits<double>::max();
    maxY = std::numeric_limits<double>::min();
    for (int j = 0; j < ui->customPlot->graphCount(); j++) {
        QCPGraph *graph = ui->customPlot->graph(j);
        if (graph->dataCount() == 0) {
            continue;
        }
        if (graph->valueAxis() != yAxis) {
            continue;
        }
        QCPGraphDataContainer::const_iterator it = graph->data().constBegin();
        for (; it != graph->data().constEnd(); ++it) {
            double value = it->value;
            if (value < minY) {
                minY = value;
            }
            if (value > maxY) {
                maxY = value;
            }
        }
    }
}

3. 计算自适应的范围，并设置每个y轴的范围。

double range = qMax(qAbs(minY), qAbs(maxY)) * 2;
double center = (minY + maxY) / 2;
for (int i = 0; i < yAxisList.length(); i++) {
    QCPAxis *yAxis = yAxisList[i];
    yAxis->setRange(center - range, center + range);
}

完整代码示例：

QList<QCPAxis*> yAxisList;
for (int i = 0; i < ui->customPlot->axisRectCount(); i++) {
    QCPAxisRect *axisRect = ui->customPlot->axisRect(i);
    QCPAxis *yAxis = axisRect->axis(QCPAxis::atLeft);
    if (yAxis != nullptr) {
        yAxisList.append(yAxis);
    }
}
for (int i = 0; i < yAxisList.length(); i++) {
    QCPAxis *yAxis = yAxisList[i];
    double minY = std::numeric_limits<double>::max();
    double maxY = std::numeric_limits<double>::min();
    for (int j = 0; j < ui->customPlot->graphCount(); j++) {
        QCPGraph *graph = ui->customPlot->graph(j);
        if (graph->dataCount() == 0) {
            continue;
        }
        if (graph->valueAxis() != yAxis) {
            continue;
        }
        QCPGraphDataContainer::const_iterator it = graph->data().constBegin();
        for (; it != graph->data().constEnd(); ++it) {
            double value = it->value;
            if (value < minY) {
                minY = value;
            }
            if (value > maxY) {
                maxY = value;
            }
        }
    }
    double range = qMax(qAbs(minY), qAbs(maxY)) * 2;
    double center = (minY + maxY) / 2;
    yAxis->setRange(center - range, center + range);
}