最优化方法程序作业专业：油气储运工程班级：姓名：学号：一、开发工具该应用程序采用的开发工具是Visual studio 2005，编程语言使用的是C#。

二、程序代码（1）0.618法和抛物线法求ψ(t)=sint，初始点t0=1①主程序：using System;using System.Data;using System.Configuration;using System.Web;using System.Web.Security;using System.Web.UI;using System.Web.UI.WebControls;using System.Web.UI.WebControls.WebParts;using System.Web.UI.HtmlControls;using System.Collections;public partial class_Default : System.Web.UI.Page{JiSuan JS = new JiSuan();protected void Button1_Click(object sender, EventArgs e){double xx0 = 0.01;//步长double tt0 = 1, pp = 2, qq = 0.5;ArrayList list1 = new ArrayList();list1 = (ArrayList)JS.SuoJian(xx0, tt0, pp, qq);//调用倍增半减函数double aa = double.Parse(list1[0].ToString());double bb = double.Parse(list1[1].ToString());txtShangxian.Text = bb.ToString();//在页面上显示极小区间txtXiaxian.Text = aa.ToString();ArrayList list2 = new ArrayList();list2 = (ArrayList)JS.JiXiao1(aa, bb);//调用0.618法函数double jixiao1 = double.Parse(list2[0].ToString());double fjixiao1 = double.Parse(list2[1].ToString());txtJixiao1.Text = jixiao1.ToString();//在页面上显示极小点txtFjixiao1.Text = fjixiao1.ToString();//在页面上显示极小点处的函数值ArrayList list3 = new ArrayList();list3 = (ArrayList)JS.JiXiao2(aa, bb);//调用抛物线法函数double jixiao2 = double.Parse(list3[0].ToString());double fjixiao2 = double.Parse(list3[1].ToString());txtJixiao2.Text = jixiao2.ToString();//在页面上显示极小点txtFjixiao2.Text = fjixiao2.ToString();//在页面上显示极小点处的函数值 }}②各个子函数的程序：using System;using System.Data;using System.Configuration;using System.Web;using System.Web.Security;using System.Web.UI;using System.Web.UI.WebControls;using System.Web.UI.WebControls.WebParts;using System.Web.UI.HtmlControls;using System.Collections;///<summary>/// JiSuan 的摘要说明///</summary>public class JiSuan{public JiSuan(){//// TODO: 在此处添加构造函数逻辑//}//目标函数public double f(double z){double zz = Math.Sin(z);return zz;}//倍增半减函数public ArrayList SuoJian(double x0, double t0, double p, double q){double t1;double f0, f1;double x1, t2;double f2;double a = 0, b = 0, c = 0;double fa, fc, fb;double t3, f3;bool biaozhi1 = true;//设置是否循环的标志bool biaozhi2 = true;t1 = t0 + x0;f0 = f(t0);//调用目标函数f1 = f(t1);if (f0 > f1){while (biaozhi1){x1 = p * x0;t2 = t1 + x1;f2 = f(t2);//调用目标函数if (f1 > f2){t0 = t1;t1 = t2;f0 = f1;f1 = f2;continue;}else{a = t0;c = t1;b = t2;fa = f0;fc = f1;fb = f2;break;}}}else{t3 = t1;f3 = f1;t1 = t0;f1 = f0;t0 = t3;f0 = f3;while (biaozhi2){x1 = q * x0;t2 = t1 - x1;f2 = f(t2);//调用目标函数if (f1 > f2){t0 = t1;t1 = t2;f0 = f1;f1 = f2;continue;}else{a = t2;c = t1;b = t0;fa = f2;fc = f1;fb = f0;break;}}}ArrayList list = new ArrayList();list.Add(a);list.Add(b);return list;}//0.618法函数public ArrayList JiXiao1(double a, double b) {double jd = 0.0001;//精度double p = 0.618;double t1, t2;double f1, f2;double jixiao=0;//极小点bool biaozhi1 = true;//设置是否循环标志bool biaozhi2 = true;while (biaozhi1){t1 = a + (1 - p)*(b - a);t2 = a + p * (b - a);f1 = f(t1);//调用目标函数f2 = f(t2);while (biaozhi2){if (f1 < f2){b = t2;t2 = t1;f2 = f1;t1 = a + (1 - p)*(b - a); f1 = f(t1);//调用目标函数if (Math.Abs(b - a) > jd) {continue;}else{biaozhi1 = false;break;}}else if (f1 == f2){a = t1;b = t2;if (Math.Abs(b - a) > jd) {break;}else{biaozhi1 = false;break;}}else if (f1 > f2){a = t1;t1 = t2;f1 = f2;t2 = a + p * (b - a);f2 = f(t2);//调用目标函数if (Math.Abs(b - a) > jd){continue;}else{biaozhi1 = false;break;}}}}jixiao = (a + b) / 2;double fjixiao = f(jixiao);//调用目标函数ArrayList list = new ArrayList();list.Add(jixiao);list.Add(fjixiao);return list;}//抛物线法函数public ArrayList JiXiao2(double a, double b){double jd = 0.0001;//精度double c = a + (b - a) / 2;//将c的值设为a、b点的中点double fa, fb, fc, c1, c2;double jixiao = 0;//极小点double ta, fta;double fac;bool biaozhi1 = true;//设置是否循环标志while (biaozhi1){fa = f(a);//调用目标函数fb = f(b);fc = f(c);c1 = (fb - fa) / (b - a);c2 = ((fc - fa) / (c - a) - c1) / (c - b);if (c2 == 0){jixiao = c;break;}else{ta = 0.5 * (a + b - (c1 / c2));fta = f(ta);//调用目标函数if (Math.Abs(b - a) <= jd){jixiao = ta;break;}else{if (fc > fta){if (c > ta){b = c;fb = fc;c = ta;fc = fta;continue;}else{a = c;fa = fc;c = ta;fc = fta;continue;}}else if (fc == fta){if (c > ta){a = ta;b = c;c = (c + ta) / 2;fa = fta;fb = fc;fc = f(c);//调用目标函数continue;}else if (c == ta){fac = f((a + c) / 2);//调用目标函数if (fac < fc){c = (a + c) / 2;fc = f(c);//调用目标函数b = ta;fb = fta;continue;}else{a = (a + c) / 2;fa = f(a);//调用目标函数continue;}}else if (c < ta){a = c;c = (c + ta) / 2;b = ta;fa = fc;fb = fta;fc = f(c);//调用目标函数continue;}}else if (fc < fta){if (c > ta){a = ta;fa = fta;continue;}else{b = ta;fb = fta;continue;}}}}}double fjixiao = f(jixiao);//调用目标函数ArrayList list = new ArrayList();list.Add(jixiao);list.Add(fjixiao);return list;}}（2）共轭梯度法求函数极小点：f(x)=1.5x12+0.5x22-x1x2-2x1；初始点为（-2，4）①主程序：using System;using System.Data;using System.Configuration;using System.Web;using System.Web.Security;using System.Web.UI;using System.Web.UI.WebControls;using System.Web.UI.WebControls.WebParts;using System.Web.UI.HtmlControls;using System.Collections;public partial class_Default : System.Web.UI.Page{JiSuan JS = new JiSuan();protected void Button1_Click(object sender, EventArgs e){//共轭梯度法求极小值double[] x0 = new double[2];//定义二维数组double[] x = new double[2];x0[0] = -2;x0[1] = 4;double x00 = -2;double x01 = 4;double jd = 0.0001;//精度bool biaozhi1 = true;//设置是否循环的标志bool biaozhi2 = true;double y;//定义关于x的函数值double[] g = new double[2];//定义函数在点x处的梯度值double[] p = new double[2];double ggm, ggo=0;double jixiao;double x1=0, x2=0, fy=0;int i;for (int j = 0; j < 2; j++){x[j] = x0[j];}while (biaozhi1){i = 0;while (biaozhi2){y = JS.f(x[0], x[1]);//调用目标函数g[0] = JS.g0(x[0], x[1]);//调用梯度函数，求在点x处的梯度值 g[1] = JS.g1(x[0], x[1]);ggm = g[0] * g[0] + g[1] * g[1];if (ggm <= jd){x1 = x[0];x2 = x[1];fy = y;biaozhi1 = false;break;}else{if (i == 0){p[0] = -g[0];p[1] = -g[1];}else{p[0] = -g[0] + (ggm / ggo) * p[0];p[1] = -g[1] + (ggm / ggo) * p[1];}//调用0.618法子函数，找出极小点jixiao = JS.JiXiao1(x[0], x[1], p[0], p[1], x00, x01); x[0] = x[0] + jixiao * p[0];x[1] = x[1] + jixiao * p[1];ggo = ggm;i++;if (i >= 2){break;}else{continue;}}}}txtx1.Text = x1.ToString();txtx2.Text = x2.ToString();txty.Text = fy.ToString();}}②子函数程序：using System;using System.Data;using System.Configuration;using System.Web;using System.Web.Security;using System.Web.UI;using System.Web.UI.WebControls;using System.Web.UI.WebControls.WebParts;using System.Web.UI.HtmlControls;using System.Collections;///<summary>/// JiSuan 的摘要说明///</summary>public class JiSuan{public JiSuan(){//// TODO: 在此处添加构造函数逻辑//}//目标函数public double f(double z1,double z2){double zz = 1.5 * z1 * z1 + 0.5 * z2 * z2 - z1 * z2 - 2 * z1;return zz;}//求梯度值函数public double g0(double z1, double z2){double zz = 3 * z1 - z2 - 2;return zz;}public double g1(double z1, double z2){double zz = z2 - z1;return zz;}//倍增半减函数public ArrayList SuoJian(double x0, double t0, double p, double q, double xx0, double xx1, double p0, double p1,double x00,double x01){double t1;double f0, f1;double x1, t2;double f2;double a = 0, b = 0, c = 0;double fa, fc, fb;double t3, f3;bool biaozhi1 = true;//设置是否循环的标志bool biaozhi2 = true;double x_0t1, x_1t1, x_0t2, x_1t2;x_0t1 = xx0 + t1 * p0;x_1t1 = xx1 + t1 * p1;f0 = f(x00, x01);//调用目标函数f1 = f(x_0t1, x_1t1);if (f0 > f1){while (biaozhi1){x1 = p * x0;t2 = t1 + x1;x_0t2 = x_0t1 + t2 * p0;x_1t2 = x_1t1 + t2 * p1;f2 = f(x_0t2, x_1t2);//调用目标函数if (f1 > f2){t0 = t1;t1 = t2;f0 = f1;f1 = f2;continue;}else{a = t0;c = t1;b = t2;fa = f0;fc = f1;fb = f2;break;}}}else{t3 = t1;f3 = f1;t1 = t0;f1 = f0;t0 = t3;while (biaozhi2){x1 = q * x0;t2 = t1 - x1;x_0t2 = x_0t1 + t2 * p0;x_1t2 = x_1t1 + t2 * p1;f2 = f(x_0t2, x_1t2);//调用目标函数if (f1 > f2){t0 = t1;t1 = t2;f0 = f1;f1 = f2;continue;}else{a = t2;c = t1;b = t0;fa = f2;fc = f1;fb = f0;break;}}}ArrayList list = new ArrayList();list.Add(a);list.Add(b);return list;}//0.618法函数public double JiXiao1(double x0, double x1, double p0, double p1,double x00,double x01){double jd = 0.0001;//精度double p = 0.618;double t1, t2;double jixiao = 0;//极小点bool biaozhi1 = true;//设置是否循环标志bool biaozhi2 = true;double xx0 = 0.01;//步长double tt0 = 0, pp = 2, qq = 0.5;double x_0t1, x_1t1, x_0t2, x_1t2;ArrayList list1 = new ArrayList();//调用倍增半减函数获取极小区间list1 = (ArrayList)SuoJian(xx0, tt0, pp, qq, x0, x1, p0, p1, x00, x01);double a = double.Parse(list1[0].ToString());double b = double.Parse(list1[1].ToString());while (biaozhi1){t1 = a + (1 - p) * (b - a);t2 = a + p * (b - a);x_0t1 = x00 + t1 * p0;x_1t1 = x01 + t1 * p1;x_0t2 = x_0t1 + t2 * p0;x_1t2 = x_1t1 + t2 * p1;f1 = f(x_0t1, x_1t1);//调用目标函数f2 = f(x_0t2, x_1t2);while (biaozhi2){if (f1 < f2){b = t2;t2 = t1;f2 = f1;t1 = a + (1 - p) * (b - a);x_0t1 = x00 + t1 * p0;x_1t1 = x01 + t1 * p1;f1 = f(x_0t1, x_1t1);//调用目标函数if (Math.Abs(b - a) > jd){continue;}else{biaozhi1 = false;break;}}else if (f1 == f2){a = t1;b = t2;if (Math.Abs(b - a) > jd){break;}else{biaozhi1 = false;break;}}else if (f1 > f2){a = t1;t1 = t2;f1 = f2;t2 = a + p * (b - a);x_0t2 = x_0t1 + t2 * p0;x_1t2 = x_1t1 + t2 * p1;f2 = f(x_0t2, x_1t2);//调用目标函数if (Math.Abs(b - a) > jd){continue;}else{biaozhi1 = false;break;}}}}jixiao = (a + b) / 2;return jixiao;}}三、程序运行界面及结果（1）0.618法和抛物线法求ψ(t)=sint，初始点t0=1（2）共轭梯度法求函数极小点：f(x)=1.5x12+0.5x22-x1x2-2x1；初始点为（-2，4）。