大连理工大学优化方法上机大作业.docx

1、大连理工大学优化方法上机大作业 2016年大连理工大学优化方法上机大作业学院：专业：班级：学号：姓名：上机大作业1：1.最速下降法：function f = fun(x) f = (1-x(1)2 + 100*(x(2)-x(1)2)2; endfunction g = grad(x) g = zeros(2,1); g(1)=2*(x(1)-1)+400*x(1)*(x(1)2-x(2); g(2) = 200*(x(2)-x(1)2); end function x_star = steepest(x0,eps) gk = grad(x0); res = norm(gk); k = 0;

2、while res eps & k f0 + *ak*slope ak = ak/4; xk = x0 + ak*dk; f1 = fun(xk); end k = k+1; x0 = xk; gk = grad(xk);res = norm(gk); fprintf(-The %d-th iter, the residual is %fn,k,res); end x_star = xk; end clear x0=0,0; eps=1e-4; x=steepest(x0,eps)2.牛顿法：function f = fun(x) f = (1-x(1)2 + 100*(x(2)-x(1)2)

3、2; endfunction g = grad2(x) g = zeros(2,2); g(1,1)=2+400*(3*x(1)2-x(2); g(1,2)=-400*x(1); g(2,1)=-400*x(1); g(2,2)=200; end function g = grad(x) g = zeros(2,1); g(1)=2*(x(1)-1)+400*x(1)*(x(1)2-x(2); g(2) = 200*(x(2)-x(1)2); end function x_star = newton(x0,eps) gk = grad(x0); bk = grad2(x0)(-1); res

4、= norm(gk); k = 0; while res eps & k clear x0=0,0; eps=1e-4; x1=newton(x0,eps)-The 1-th iter, the residual is -The 2-th iter, the residual is x1 = 法：function f = fun(x) f = (1-x(1)2 + 100*(x(2)-x(1)2)2; endfunction g = grad(x) g = zeros(2,1); g(1)=2*(x(1)-1)+400*x(1)*(x(1)2-x(2); g(2) = 200*(x(2)-x(

5、1)2); end function x_star = bfgs(x0,eps) g0 = grad(x0); gk=g0; res = norm(gk); Hk=eye(2); k = 0; while res eps & k f0 + *ak*slope ak = ak/4; xk = x0 + ak*dk; f1 = fun(xk); end k = k+1; fa0=xk-x0; x0 = xk; go=gk;gk = grad(xk);y0=gk-g0;Hk=(eye(2)-fa0*(y0)/(fa0)*(y0)*(eye(2)-(y0)*(fa0)/(fa0)*(y0)+(fa0*

6、(fa0)/(fa0)*(y0);res = norm(gk); fprintf(-The %d-th iter, the residual is %fn,k,res); end x_star = xk; End clear x0=0,0; eps=1e-4; x=bfgs(x0,eps)4.共轭梯度法： function f = fun(x) f = (1-x(1)2 + 100*(x(2)-x(1)2)2; endfunction g = grad(x) g = zeros(2,1); g(1)=2*(x(1)-1)+400*x(1)*(x(1)2-x(2); g(2) = 200*(x(

7、2)-x(1)2); end function x_star =CG(x0,eps) gk = grad(x0);res = norm(gk); k = 0; dk = -gk; while res eps & k f0 + *ak*slope ak = ak/4; xk = x0 + ak*dk; f1 = fun(xk); end k = k+1; x0 = xk; g0=gk; gk = grad(xk);res = norm(gk);p=(gk/g0)2;dk1=dk;dk=-gk+p*dk1;fprintf(-The %d-th iter, the residual is %fn,k

8、,res); end x_star = xk; end clear x0=0,0; eps=1e-4; x=CG(x0,eps)上机大作业2：function f= obj(x)f=4*x(1)-x(2)2-12;endfunction h,g =constrains(x)h=x(1)2+x(2)2-25;g=zeros(3,1);g(1)=-10*x(1)+x(1)2-10*x(2)+x(2)2+34;g(2)=-x(1);g(3)=-x(2);endfunction f=alobj(x) %拉格朗日增广函数%N_equ等式约束个数?%N_inequ不等式约束个数N_equ=1;N_ineq

9、u=3;global r_al pena;%全局变量h_equ=0;h_inequ=0;h,g=constrains(x);%等式约束部分?for i=1:N_equ h_equ=h_equ+h(i)*r_al(i)+(pena/2)*h(i).2;end %不等式约束部分for i=1:N_inequ h_inequ=h_inequ+pena)*(max(0,(r_al(i)+pena*g(i).2-r_al(i).2);end%拉格朗日增广函数值f=obj(x)+h_equ+h_inequ;function f=compare(x) global r_al pena N_equ N_ine

10、qu;N_equ=1;N_inequ=3;h_inequ=zeros(3,1);h,g=constrains(x);%等式部分for i=1:1 h_equ=abs(h(i); end%不等式部分 for i=1:3h_inequ=abs(max(g(i),-r_al(i+1)/pena);endh1 = max(h_inequ);f= max(abs(h_equ),h1); %sqrt(h_equ+h_inequ);function x,fmin,k =almain(x_al)%本程序为拉格朗日乘子算法示例算法%函数输入：% x_al:初始迭代点% r_al：初始拉格朗日乘子N-equ:等式

11、约束个数N_inequ:不等式约束个数?%函数输出% X：最优函数点FVAL:最优函数值%=程序开始=global r_al pena ; %参数（全局变量）pena=10; %惩罚系数r_al=1,1,1,1;c_scale=2; %乘法系数乘数cta=; %下降标准系数e_al=1e-4; %误差控制范围max_itera=25;out_itera=1; %迭代次数%=算法迭代开始=while out_iteramax_itera x_al0=x_al; r_al0=r_al; %判断函数? compareFlag=compare(x_al0); %无约束的拟牛顿法BFGS X,fmin=

12、fminunc(alobj,x_al0); x_al=X; %得到新迭代点 %判断停止条件? if compare(x_al)e_al disp(we get the opt point); break end %c判断函数下降度? if compare(x_al)cta*compareFlag pena=1*pena; %可以根据需要修改惩罚系数变量 else pena=min(1000,c_scale*pena); %乘法系数最大1000 disp(pena=2*pena); end %?更新拉格朗日乘子 h,g=constrains(x_al); for i=1:1 %等式约束部分 r_al(i)= r_al0(i)+pena*h(i); end for i=1:3 %不等式约束部分 r_al(i+1)=max(0,(r_al0(i+