梯度下降法.doc

西安电子科技大学电子工程学院 最优化方法及应用（1）上机报告题 目： 最速下降法求最优解 任课老师：_ _xxxxxx_ _姓 名：_ xxxxxx_ _学 号:_ _xxxxxxxx_ _班 级：_ 02951_ _ _一、问题叙述：编程求解函数：的最小值点及最小值。二、问题分析实现方法：最速下降法（C语言）其中一维线性搜索用黄金分割法。三、代码/ 1_Steep.cpp : Defines the entry point for the console application./用最速下降法求解minf(X)=minf(x)=(x1+10*x2)2+5(x3-x4)2+(x2-2*x3)4+10(x1-x4)4,e=0.001。#include stdafx.h#include#includeusing namespace std;#define _accuracy 0.001/plusx()/*void plusx(float x4,float g4,float t)x0 += t*g0;x1 += t*g1;x2 += t*g2;x3 += t*g3;*/* f() */float f(float x4)float sum = 0.0;sum += (x0+10*x1)*(x0+10*x1);sum += 5*(x2-x3)*(x2-x3);sum += (x1-2*x2)*(x1-2*x2)*(x1-2*x2)*(x1-2*x2);sum += 10*(x0-x3)*(x0-x3)*(x0-x3)*(x0-x3);return sum;/void plusx(float x14,float x04,float g4,float t)x10 = x00+t*g0;x11 = x01+t*g1;x12 = x02+t*g2;x13 = x03+t*g3;/searchRange()void searchRange(float &a,float &b,float x4,float g4)float t0=10,t1=10,t2=2;float h=1;float xi=2;float f0,f1;float x14;int k=0;while (1)f0 = f(x);t2 = t1+h;plusx(x1,x,g,t2);f1 = f(x1);if (f1f0)h = xi*h;t0 = t1;t1 = t2;f0 = f1;k+;continue;else if(0=k)h = -h;t0 = t2;continue;else a=(t0=t2?t0:t2);b=(t0=t2?t2:t0);break;/gold()void gold(float &a,float &b,float x4,float g4)float t1,t2;float x14,x24;t2=a+0.382*(b-a);plusx(x2,x,g,t2);t1=a+b-t2;plusx(x1,x,g,t1);float f1,f2;f1=f(x1);f2=f(x2);if(f1f2) b=t1;else a=t2;b=t1; /* grad() */int grad(float X4,float g4)g0=2*(X0+10*X1)+40*(X0-X3)*(X0-X3)*(X0-X3);g1=20*(X0+10*X1)+4*(X1-2*X2)*(X1-2*X2)*(X1-2*X2);g2=10*(X2-X3)-8*(X1-2*X2)*(X1-2*X2)*(X1-2*X2);g3=0-10*(X2-X3)-40*(X0-X3)*(X0-X3)*(X0-X3);/*float sum = g0+g1+g2+g3;g0 = g0/sum;g1 = g1/sum;g2 = g2/sum;g3 = g3/sum;*/return 0;/* linesearch() */int linesearch(float Xk14,float Xk04,float g4)float mina,maxb,Lanbuda;/*searchRange(mina,maxb,Xk0,g);*/mina = -100;maxb =100;while (maxb-mina_accuracy) gold(mina,maxb,Xk0,g);Lanbuda = (mina+maxb)/2;plusx(Xk1,Xk0,g,Lanbuda);return 0;/*main()*/int main(int argc, char* argv)float X04=10,10,10,10,X14=10,10,10,10;float f0,f1,g4;f0=f(X0);grad(X0,g);int k=0;while(1)if(0=g0*g0+g1*g1+g2*g2+g3*g3) break;linesearch(X1,X0,g);f1=f(X1);grad(X1,g);if (_accuracy=g0*g0+g1*g1+g2*g2+g3*g3) break;X00 = X10;X01 = X11;X02 = X12;X03 = X13;/*if(k20)printf(迭代次数%d:tX=%.3f,%.3f,%.3f,%.3ft,+k,X00,X01,X02,X03);printf(minf(X)=%.3fn,f1);*/printf(迭代次数%d:tX=%.3f,%.3f,%.3f,%.3ft,+k,X00,X01,X02,X03);printf(minf(X)=%.3fn,f1);f0=f1;printf(target:X=%.3f,%.3f,%.3f,%.3fn,X00,X01,X02,X03);printf(minf(X)=%.3fn,f1);/cout.unsetf(ios:scientific);/coutX=setprecision(1)X10,setprecisio