C#二分法求函数极值

采用二分法求函数极大值和极小值。

xaml代码：

    <Grid>
        <StackPanel>
            <Button  Name="colum" Width="120" Height="30" Margin="30,30,0,0" Click="colum_Click">计算最大值</Button>
            <TextBox Name="result" Width="120" Height="30" Margin="30,10,0,0"></TextBox>
            <Button Name="colum2" Width="120" Height="30" Margin="30,30,0,0" Click="colum2_Click">计算最小值</Button>
            <TextBox Name="result2" Width="120" Height="30" Margin="30,10,0,0"></TextBox>
        </StackPanel>
    </Grid>

自定义函数：

static double TargetFunction(double x)
        {
            // 示例函数:
            return x * x*x-x-2;
        }

二分法求极大值代码：

        // 使用二分法寻找函数的最大值
        static double FindMaximumWithBinarySearch(double start, double end, double tolerance)
        {
            double mid;
            
            while (end - start > tolerance)
            {
                if(TargetFunction(start)< TargetFunction(end))
                {
                    mid = (end + start) / 2;

                    if(TargetFunction(mid) < TargetFunction(end))
                    {
                        start=mid;
                    }
                    else
                    {
                        start = mid;
                    }
                }

                else
                {
                    mid = (end + start) / 2;

                    if (TargetFunction(mid) < TargetFunction(end))
                    {
                        end = mid;
                    }
                    else
                    {
                        end= mid;
                    }
                }
                
            }

            return TargetFunction((start+end)/2);
        }

二分法求极小值代码：

        // 使用二分法寻找函数的最小值
        static double FindMinmumWithBinarySearch(double start, double end, double tolerance)
        {
            double mid;

            while (end - start > tolerance)
            {
                mid = (start + end) / 2;

                if (TargetFunction(start) < TargetFunction(end))
                {
                    if (TargetFunction(start) < TargetFunction(mid))
                    {
                        end = mid;

                    }

                    else
                    {
                        end = mid;


                    }
                }

                else
                {
                    if (TargetFunction(end) < TargetFunction(mid))
                    {
                        start = mid;
                    }

                    else
                    {
                        start = mid;
                    }
                }

            }
            return TargetFunction((start+end)/2);

        }

按钮“计算最大值”实例代码：

        private void colum_Click(object sender, RoutedEventArgs e)
        {
            // 起始点和结束点
            double start = -2;

            double end = 10;

            // 精度
            double epsilon = 0.00001;

            // 求解
            double maximum = FindMaximumWithBinarySearch(start, end, epsilon);

            result.Text = maximum.ToString();

        }

按钮“计算最小值”实例代码：

        private void colum2_Click(object sender, RoutedEventArgs e)
        {
            double start = -2;

            double end = 10;

            double tolerance = 0.00001; // 容忍度

            double minum = FindMinmumWithBinarySearch(start, end, tolerance);
            
            result2.Text= minum.ToString();  
        }

计算结果显示：