0.618法牛顿法Powell法优化设计MATLAB程序设计.docVIP

机械优化设计 姓 名： 李 红 昊 学 号：152085201184 班 级：机械工程15班 1.用0.618法求一元函数f（t）=t^2+2*t在区间[-3,5]中的极小点，要求计算到区间的长度小于0.05。 用MATLAB编程如下： function [x,minf]=minHJ(f,a,b,eps) format long; if nargin==3 eps=0.05; end l=a+0.382*(b-a); u=a+0.618*(b-a); k=1; tol=b-a; while toleps k100000 fl=subs(f,findsym(f),l); fu=subs(f,findsym(f),u); if flfu a=l; l=u; u=a+0.618*(b-a); else b=u; u=l; l=a+0.382*(b-a); end k=k+1; tol=abs(b-a); end if k==100000 disp; x=NaN; minf=NaN; return; end x=(a+b)/2; minf=subs(f,findsym(f),x); minf = double(minf); format short; syms t; f=t^2+2*t; [x,fx]=minHJ(f,-3,5,eps) 运行结果： 2.用牛顿法求函数f = x1^2 + 4*x2^2 + x3^2 - 2*x1 + 18*x3的极小点。 用MATLAB编程如下: function [diff_x] = function_c1(x1,x2,x3) syms x1 x2 x3 f = x1^2 + 4*x2^2 + x3^2 - 2*x1 + 18*x3; diff_x1 = diff(f,x1); diff_x2 = diff(f,x2); diff_x3 = diff(f,x3); diff_x = [diff_x1; diff_x2; diff_x3]; return end function [H] = function_c2(x1,x2,x3) syms x1 x2 x3 f = x1^2 + 4*x2^2 + x3^2 - 2*x1 + 18*x3; diff_x1 = diff(f,x1); diff_x2 = diff(f,x2); diff_x3 = diff(f,x3); diff_x1_x1 = diff(diff_x1,x1); diff_x2_x2 = diff(diff_x2,x2); diff_x3_x3 = diff(diff_x3,x3); diff_x1_x2 = diff(diff_x1,x2); diff_x1_x3 = diff(diff_x1,x3); diff_x2_x1 = diff_x1_x2; diff_x2_x3 = diff(diff_x2,x3); diff_x3_x1 = diff_x1_x3; diff_x3_x2 = diff_x2_x3; H = [diff_x1_x1 diff_x1_x2 diff_x1_x3;... diff_x2_x1 diff_x2_x2 diff_x2_x3;... diff_x3_x1 diff_x3_x2 diff_x3_x3]; return end e = 1; x1 = 0; x2 = 0; x3 = 0; while e0.00001 f_d = function_c1(x1,x2,x3); f = subs(f_d, x1,x2,x3, [x1,x2,x3]); H = function_c2(x1,x2,x3); H_inv = inv(H); x = [x1;x2;x3] - H_inv * f; e = abs(x(1)-x1) / x(1); x1 = x(1); x2 = x(2); x3 = x(3); end disp(x) 运行结果： 3.用Powell法求函数f=t^2+s^2-t*s-10*t-4*s+60的最优点X*=[t,s]T。计算收敛精度eps=0.0001。 用MATLAB编程如下: function[minx,maxx]=minJT(f,x0,h0,eps) format long; if nargin==3 eps=