最速下降法报告

1、西安电子科技大学电子工程学院大作业(-)科目：最优化方法及其应用任课老师：姓名：学号：班级：题目运用梯度下降法(最速下降法)求解优化问题问题叙述用梯度下降法来求解优化问题mif =(x +10v )2 + 5(x -x )2 + (x - 2x )4 +1C(x -x )4其中一维搜索可用0.618法方法介绍最速下降法的步骤：1、取初始点x 0和允许误差分0，令k=02、计算 p( k) = -Vf (x (k)3、若p(k) 则停止，取x孚x(k)；否则，转(4)4、求a k 0使f (x(k) +a p(k) = minf (x(k) +Op(k)ka05 令 x(k+1) = x(k)

2、+ a p(k) k : k +1 转(2)U、k，方法的原理易于理解，但是用软件实现过程则有一 定的难度了，特别是对于0.618法的运用。如果思路不 够清晰，又或者不能做到一气呵成，则很容易出错，以 至于不得不重头开始思考。在编程过程中，程序不可能 体会 没有问题，知道问题所在怎么也能解决了，可是怕就怕 在不知道问题出在了哪里。这个时候就需要我们认真仔 细的检查代码，结合软件提示的信息对代码进行修改。 自认为在这次编程的修改过程中，一定不能因为出错就 一个冲动的修改代码，或许所修改的并不是错误的根 源，结果可能错误变得越来越多，悔不当初。代码 语言选择：Microsoft Visual St

3、udio2010(C+)(在此处填入代码)#include stdio.h#include stdlib.h#include math.h”double func( double *x )return(x0+10*x1)*(x0+10*x1) + 5*(x2-x3)*(x2-x3) + (x1-2*x2)*(x1-2*x2)*(x1-2*x )*(x1-2*x2) + 10*(x0-x3)*(x0-x3)*(x0-x3)*(x0-x3);double norm ( double *x ) /范数returnsqrt ( x0*x0+x1*x1+x 2 *x +x3*x3);void vgran

4、d( double*p ,double *x ) 负梯度p0 = -2*(x0+10*x1) - 40*(x0-x3)*(x0-x3)*(x0-x3);p1 = -20*(x0+10*x1) - 4*(x1-2*x 2 )*(x1-2*x 2 )*(x1-2*x 2);p2 = -10*(x 2 -x3) + 8*(x1-2*x 2 )*(x1-2*x 2 )*(x1-2*x2);p3 = 10*(x 2-x3) + 40*(x0-x3)*(x0-x3)*(x0-x3);double goldf (double t, double*p, double *x) /gold辅助函数double x

5、tmp4;for (int i=0; i!=4; +i)xtmpi=xi+pi*t;return func(xtmp);double gold (double begin ,double end, double t2, double *p, double *x ) /0.618法while (1)double t1=0.382*(end-begin)+begin, e=0.01;if(fabs(t1-t2)e)return (t1+t2)/2;else if(goldf(t1,p,x) goldf(t2,p,x)end=t2;t2=t1;elsebegin=t1;t2=0.618*(end-b

6、egin)+begin; int main()double x4, p4, t, a ,e=0.01;x0=0.1, x1=0.1, x2=0.1, x3=0.1;int count=0;printf(min f(x)=(x1+10*x2)A2+5*(x3-x4)A2+(x2-2*x3)A4+10*(x1-x4)A4n);printf(using 0.618 algorithmn);printf(begin=-50,end=50,t2=11.8);printf(initialize x1=0.1,x2=0.1,x3=0.1,x4=0.1n);printf(initialize precisio

7、n: e=0.01nn);while(1)vgrand( p, x );if ( a=norm( p ), a = e )printf(最优解为：x1=%lf , x2=%lf , x3=%lf ,x4=%lfn,x0,x1,x 2 ,x3);return 0;printf(count=%dn”,count);count=count+1;printf(x1=%lf , x2=%lf , x3=%lf , x4=%lfn”,x0,x1,x 2 ,x3);t=gold(-50,50,11.8,p, x);for (int i=0; i!=4; +i)xi=xi+t*pi;min运行结果及分析f(x

8、) = (x1+10*x2)”2+5*(x3-x4)”2+(x2-2*x3)”4+10*(x1-x4)”4using 0.618 algorithmbegin=-50,end=50,t2=11.8initializex1=0.1,x2=0.1,x3=0.1,x4=0.1initialize precision: e=0.01 count=0 x1=0.100000 , x2=0.100000 , x3=0.100000 , x4=0.100000count=1x1=0.092222 , x2=0.022239 , x3=0.099972 , x4=0.100000count=2x1=0.089

9、998 , x2=0.000074 , x3=0.099814 , x4=0.099999count=3x1=0.089303 , x2=-0.006753 , x3=0.099578 , x4=0.099992count=4x1=0.089083 , x2=-0.008784 , x3=0.099245 , x4=0.099970 x4=0.099437x4=0.099191x4=0.091033x4=0.091121x4=0.091130 x4=0.091077x4=0.090977x4=0.090910 x4=0.089027x4=0.088799x4=0.084484x4=0.0844

10、66x4=0.084404x4=0.084308x4=0.084185count=6x1=0.088815 ,count=7x1=0.088356 ,count=8x1=0.088189 ,count=9x1=0.088310 ,count=10 x1=0.088119 ,count=11 x1=0.088268 ,count=12x1=0.088160 ,count=13 x1=0.087884 ,count=14x1=0.087811 ,count=15x1=0.087618 ,count=16 x1=0.087532 ,count=17 x1=0.087578 ,count=18 x1=

11、0.087481 ,count=19 x1=0.087541 ,x2=-0.008005 ,x2=-0.008747 ,x2=-0.008030 ,x2=-0.009402 ,x2=-0.007907 ,x2=-0.009535 ,x2=-0.007760 ,x2=-0.008709 ,x2=-0.008065 ,x2=-0.008686 ,x2=-0.008342 ,x2=-0.008980 ,x2=-0.008284 ,x2=-0.009041 ,x2=-0.008214 ,x3=0.094577 ,x3=0.094513 ,x3=0.091880 ,x3=0.091210 ,x3=0.0

12、90618 ,x3=0.090112 ,x3=0.089648 ,x3=0.089450 ,x3=0.084522 ,x3=0.084525 ,x3=0.084305 ,x3=0.083866 ,x3=0.083472 ,x3=0.083124 ,x3=0.082801 ,x4=0.084043x4=0.083884x4=0.083801x4=0.078369x4=0.078162x4=0.075570 x4=0.075493x4=0.075398x4=0.075290 x4=0.075170 x4=0.075043x4=0.074909x4=0.074841x4=0.070629count=

13、20 x1=0.087429 , x2=-0.009112 , x3=0.082511 ,count=21x1=0.087506 , x2=-0.008132 , x3=0.082233 ,count=22x1=0.087443 , x2=-0.008655 , x3=0.082108 ,count=23x1=0.086869 , x2=-0.007761 , x3=0.074278 ,count=24x1=0.086775 , x2=-0.008622 , x3=0.074331 ,count=25x1=0.086698 , x2=-0.008316 , x3=0.074817 ,count

14、=26x1=0.086624 , x2=-0.008884 , x3=0.074569 ,count=27x1=0.086670 , x2=-0.008264 , x3=0.074339 ,count=28x1=0.086586 , x2=-0.008936 , x3=0.074129 ,count=29x1=0.086643 , x2=-0.008202 , x3=0.073928 ,count=30 x1=0.086547 , x2=-0.008999 , x3=0.073742 ,count=31x1=0.086617 , x2=-0.008130 , x3=0.073560 ,coun

15、t=32x1=0.086563 , x2=-0.008593 , x3=0.073477 ,count=33 x1=0.086152 , x2=-0.007836 , x3=0.068369 ,count=34x4=0.068839x4=0.068768x4=0.068685x4=0.068594x4=0.068497x4=0.068447x4=0.065666x4=0.065571x4=0.064172x4=0.064117x4=0.064052x4=0.063980 x4=0.063903x4=0.063821count=35 x1=0.085993 ,count=36x1=0.08592

16、3 ,count=37x1=0.085969 ,count=38x1=0.085889 ,count=39x1=0.085946 ,count=40 x1=0.085901 ,count=41x1=0.085573 ,count=42x1=0.085514 ,count=43x1=0.085432 ,count=44x1=0.085377 ,count=45x1=0.085407 ,count=46x1=0.085345 ,count=47x1=0.085383 ,count=48 x1=0.085312 ,x2=-0.008269 ,x2=-0.008826 ,x2=-0.008218 ,x

17、2=-0.008878 ,x2=-0.008158 ,x2=-0.008541 ,x2=-0.007985 ,x2=-0.008515 ,x2=-0.008298 ,x2=-0.008701 ,x2=-0.008261 ,x2=-0.008737 ,x2=-0.008217 ,x2=-0.008780 ,x3=0.068126 ,x3=0.067951 ,x3=0.067785 ,x3=0.067632 ,x3=0.067484 ,x3=0.067417 ,x3=0.063758 ,x3=0.063754 ,x3=0.063600 ,x3=0.063454 ,x3=0.063316 ,x3=0

18、.063189 ,x3=0.063067 ,x3=0.062953 ,count=50 x1=0.085320 ,count=51x1=0.084991 ,count=52 x1=0.084939 ,count=53 x1=0.084823 ,count=54 x1=0.084764 ,count=55 x1=0.084798 ,count=56 x1=0.084731 ,count=57 x1=0.084773 ,count=58 x1=0.084735 ,count=59 x1=0.084456 ,count=60 x1=0.084416 ,count=61 x1=0.084294 ,count=62 x1=0.084248 ,count=63 x1=0.084266 ,x2=-0.008165 ,x2=-0.008492 ,x2=-0.008013 ,x2=-0.008463 ,x2=-0.008226 ,x2=-0.008670 ,x2=-0.008184 ,x2=-0.008710 ,x2=-0.008136 ,x2=-0.008441 ,x2=-0.008083 ,x2=-0.008414 ,x2=-0.008244 ,x2=-0.008552 ,x2=-0.008214 ,x3=0.062841 ,x3=0.062789 ,x3=0.059964 ,x3=0.05