someoptimiummethod.txt

一些简单最优化方法的matlab实现和非线性规划算法

x0
mul_count
sum_count[/code]
happy 2006-11-17 10:12[code]%PRP重新开始计算算法(精确一维搜索,k=21,mul_count=9901,sum_count=4470,花费时间很少)
syms x1 x2;
f=50*(x2-x1^2)^2+(1-x1)^2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson)
    mul_count=mul_count+2;sum_count=sum_count+1; 
    if k==0
         p=-g1;
    else
        bta=g1'*(g1-g0)/(g0'*g0); mul_count=mul_count+5;sum_count=sum_count+4;
        if(mod(k,2))
               p=-g1+bta*p0; mul_count=mul_count+3;sum_count=sum_count+2;
        else
               p=-g1;
        end
    end
    y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
    result1=qujian(y,ar);
    b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
    result2=Asearch(y,ar,b1);
    arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
    x0=x0+arf*p;
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
    p0=p;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+7;
end;
k
x0
mul_count
sum_count[/code]
happy 2006-11-17 10:12[code]%DFP计算算法(不精确一维搜索,k=27,mul_count=2326,sum_count=1462,花费时间很少)
syms x1 x2;
f=50*(x2-x1^2)^2+(1-x1)^2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;H0=[1,0;0,1];mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson&k<1000)
    mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-H0*g1;mul_count=mul_count+7;sum_count=sum_count+4;
    else
        H1=H0-H0*yk*yk'*H0/(yk'*H0*yk)+sk*sk'/(yk'*sk);mul_count=mul_count+36;sum_count=sum_count+18;
        p=-H1*g1;mul_count=mul_count+7;sum_count=sum_count+4;
        H0=H1;
    end
    x00=x0;
    result=Usearch1(f,x1,x2,df,x0,p);
    arf=result(1);Mul=result(2);Sum=result(3);
    mul_count=mul_count+Mul;sum_count=sum_count+Sum;
    x0=x0+arf*p;
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
    p0=p;
    yk=g1-g0; sk=x0-x00;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+11;
end;
k
x0
mul_count
sum_count[/code]
happy 2006-11-17 10:12[code]%DFP计算算法(精确一维搜索,k=16,mul_count=9048,sum_count=4251花费时间很少)
syms x1 x2 ad;
f=50*(x2-x1^2)^2+(1-x1)^2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;H0=[1,0;0,1];mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson)
     mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-H0*g1;mul_count=mul_count+7;sum_count=sum_count+4;
    else
        H1=H0-H0*yk*yk'*H0/(yk'*H0*yk)+sk*sk'/(yk'*sk);mul_count=mul_count+36;sum_count=sum_count+18;
        p=-H1*g1;mul_count=mul_count+7;sum_count=sum_count+4;
        H0=H1;
    end
    x00=x0;
    y=subs(f,{x1,x2},{x0(1,1)+ad*p(1,1),x0(2,1)+ad*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
    result1=interzone(y,ad);
    b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
    result2=Goldsearch(y,ad,b1);
    arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
    x0=x0+arf*p;
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
    p0=p;
    yk=g1-g0; sk=x0-x00;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+11;
end;
k
x0
mul_count
sum_count[/code]
happy 2006-11-17 10:13[code]%DFP计算算法(精确一维搜索,k=16,mul_count=9048,sum_count=4251花费时间很少)
syms x1 x2 ar;
f=x1^2-x1*x2+x2^2+2*x1-4*x2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[2,2]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;H0=[1,0;0,1];mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson&k<=2)
     mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-H0*g1;mul_count=mul_count+7;sum_count=sum_count+4;
    else
        H1=H0-H0*yk*yk'*H0/(yk'*H0*yk)+sk*sk'/(yk'*sk);mul_count=mul_count+36;sum_count=sum_count+18;
        p=-H1*g1;mul_count=mul_count+7;sum_count=sum_count+4;
        H0=H1;
    end
    x00=x0;
    y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
    result1=qujian(y,ar);
    b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
    result2=Asearch(y,ar,b1);
    arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
    x0=x0+arf*p;
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
    p0=p;
    yk=g1-g0; sk=x0-x00;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+11;
end;
k
x0
mul_count
sum_count[/code]
happy 2006-11-17 10:13[code]%FR直接计算算法(不精确一维搜索,k=163,mul_count=32380,sum_count=20502时间略长)
syms x1 x2;
f=50*(x2-x1^2)^2+(1-x1)^2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson&k<=1000)
    mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-g1;
    else
        bta=g1'*g1/(g0'*g0); 
        p=-g1+bta*p0;
        mul_count=mul_count+7;sum_count=sum_count+4;
    end
    result=Usearch1(f,x1,x2,df,x0,p);
    arf=result(1);Mul=result(2);Sum=result(3);
    mul_count=mul_count+Mul;sum_count=sum_count+Sum;
    x0=x0+arf*p; 
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)}); 
    p0=p;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+7;
end;
k
x0
mul_count
sum_count[/code]
happy 2006-11-17 10:13[code]%FR重新开始计算算法(不精确一维搜索,k=496,mul_count=76209,sum_count=47950花费时间最长)
syms x1 x2;
f=50*(x2-x1^2)^2+(1-x1)^2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson&k<1000)
    mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-g1;
    else
        bta=g1'*g1/(g0'*g0);  mul_count=mul_count+5;sum_count=sum_count+2;
        if(mod(k,2))
               p=-g1+bta*p0;  mul_count=mul_count+3;sum_count=sum_count+2;
        else
               p=-g1;
        end
    end
    result=Usearch1(f,x1,x2,df,x0,p);
    arf=result(1);Mul=result(2);Sum=result(3);
    mul_count=mul_count+Mul;sum_count=sum_count+Sum;
    x0=x0+arf*p; 
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)}); 
    p0=p;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+7;
end;
k
x0
mul_count
sum_count[/code]
happy 2006-11-17 10:13[code]%FR重新开始计算算法(精确一维搜索,k=39,mul_count=17815,sum=7965,花费时间较少)
syms x1 x2 ar;
f=50*(x2-x1^2)^2+(1-x1)^2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson)
    mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-g1;
    else
        bta=g1'*g1/(g0'*g0);  mul_count=mul_count+5;sum_count=sum_count+2;
        if(mod(k,2))
               p=-g1+bta*p0;  mul_count=mul_count+3;sum_count=sum_count+2;
        else
               p=-g1;
        end
    end
    y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)}); mul_count=mul_count+18;sum_count=sum_count+12;
    result1=qujian(y,ar);
    b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
    result2=Asearch(y,ar,b1);
    arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
    x0=x0+arf*p;
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
    p0=p;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+7;
end;
k
x0
mul_count
sum_count[/code]
happy 2006-11-17 10:13[code]%FR直接计算算法(精确一维搜索,k=71,mul_count=31360,sum_count=13875,时间略长)
syms x1 x2 ar;
f=50*(x2-x1^2)^2+(1-x1)^2;
v=[x1,x2];
df=jacobian(f,v);
df=df.';
epson=1e-12;x0=[0,0]';g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});k=0;mul_count=0;sum_count=0;
mul_count=mul_count+7;sum_count=sum_count+4;
while(norm(g1)>epson)
    mul_count=mul_count+2;sum_count=sum_count+1;
    if k==0
         p=-g1;
    else
        bta=g1'*g1/(g0'*g0); 
        p=-g1+bta*p0;
        mul_count=mul_count+7;sum_count=sum_count+4;
    end
    y=subs(f,{x1,x2},{x0(1,1)+ar*p(1,1),x0(2,1)+ar*p(2,1)});mul_count=mul_count+18;sum_count=sum_count+12;
    result1=qujian(y,ar);
    b1=result1(1);mul_count=mul_count+result1(2);sum_count=sum_count+result1(3);
    result2=Asearch(y,ar,b1);
    arf=result2(1);mul_count=mul_count+result2(2);sum_count=sum_count+result2(3);
    x0=x0+arf*p;
    g0=g1;
    g1=subs(df,{x1,x2},{x0(1,1),x0(2,1)});
    p0=p;
    k=k+1;
    mul_count=mul_count+9;sum_count=sum_count+7;
end;
k
x0
mul_count
sum_count[/code]
happy 2006-11-17 10:29[code]%求min(x1^2+x2^2)    条件：1-x1-x2<=0
%0.618法，f=x1^2+x2^2+ck*(max(1-x1-x2),0)^2
c_jingdu=[0.001,0.001];                            
a=[0,0];
b=[20,20];                                                     %单谷搜索区间及其精度                                            
t1=[0.01,0.01];
x11=t1(1,1);
x12=t1(1,2);
t2=[9.90,9.90];                                                %最初的两个探索点                                                                                                %给出最初两个探索点
x21=t2(1,1);
x22=t2(1,2);
ck=20;                                                         %给出罚参数                                               
f1=x11^2+x12^2+ck*(max(1-x11-x12,0))^2;   
f2=x21^2+x22^2+ck*(max(1-x21-x22,0))^2;                    %给出f的初值，进而迭代 
t1=a+0.382*(b-a);
t2=a+0.618*(b-a);
N=10000;                                                       %给出迭代次数
for i=1:N
    if f1<=f2                                         
        if x21-a(1,1)<=c_jingdu(1,1)               
            break
        else
            b=t2;
            t2=t1;
            t1=a+0.382*(b-a);
            f2=f1;
            f1=x11^2+x22^2+ck*(max(1-x11-x12,0))^2;
        end
    else
        if b(1,1)-x11<=c_jingdu(1,1)
            break
        else
            a=t1;
            t1=t2;
            t2=a+0.618*(b-a);
            f1=f2;
            f2=x21^2+x22^2+ck*(max(1-x21-x22,0))^2;
        end
    end
    ck=ck*2;                                            
end
(t1+t2)/2
t1
t2[/code]
happy 2006-11-17 10:29[code]% mg0523076  潘向昱
%求min(x1^2+x2^2),约束条件1-x1-x2<=0
%0.618法
a=[0,0];
b=[10,10];                                              %确定单谷搜索[a,b]
c_wucha=[1.0e-7,1.0e-7];                                %给定最后精度c_wucha
t1=[0.1,0.1];
t2=[9.9,9.9];                                       
ck=50;                                                  %给出罚参数
f1=t1(1,1)^2+t1(1,2)^2+ck*(max(1-t1(1,1)-t1(1,2),0))^2;   
f2=t2(1,1)^2+t2(1,2)^2+ck*(max(1-t2(1,1)-t2(1,2),0))^2; %计算最初的两个探索点
t1=a+0.382*(b-a);
t2=a+0.618*(b-a);
while(1)
    if f1<=f2                                          %如果f1<f2
        if t2(1,1)-a(1,1)<=c_wucha(1,1)               
            break
        else
            b=t2;
            t2=t1;
            t1=a+0.382*(b-a);
            f2=f1;
            f1=t1(1,1)^2+t2(1,2)^2+ck*(max(1-t1(1,1)-t1(1,2),0))^2;
        end
    else
        if b(1,1)-t1(1,1)<=c_wucha(1,1)
            break
        else
            a=t1;
            t1=t2;
            t2=a+0.618*(b-a);
            f1=f2;
            f2=t2(1,1)^2+t2(1,2)^2+ck*(max(1-t2(1,1)-t2(1,2),0))^2;
        end
    end
    ck=ck*2;                                            %调整罚参数
end
(t1+t2)/2
t1
t2[/code]
yangji 2006-11-22 15:38好帖，不顶不行，多谢楼主了
liweidlut 2006-11-22 20:24好贴 哪能不顶
谢了啊
coldspring 2006-11-23 16:22太好了 ，对我的帮助就不说啦，无以用语言表达
coldspring 2006-11-23 19:2615楼   [color=Red][u][size=5]result1=interzone(y,ad); 
result2=Goldsearch(y,ad,b1);[/[/size][/u]color]在那？
楼主能不能发一下

[[i] 本帖最后由 coldspring 于 2006-11-23 19:37 编辑 [/i]]
coldspring 2006-11-23 20:02%DFP计算算法(精确一维搜索,k=16,mul_count=9048,sum_count=4251花费时间很少)
syms x1 x2 ar;
这里面的 ar 怎么解释！
suffer 2006-11-25 10:46[quote]原帖由 [i]coldspring[/i] 于 2006-11-23 19:26 发表
15楼   result1=interzone(y,ad); 
result2=Goldsearch(y,ad,b1);color]在那？
楼主能不能发一下 [/quote]

找了一下没有找到，Goldsearch估计是黄金分割搜索
suffer 2006-11-25 10:48[quote]原帖由 [i]coldspring[/i] 于 2006-11-23 20:02 发表
%DFP计算算法(精确一维搜索,k=16,mul_count=9048,sum_count=4251花费时间很少)
syms x1 x2 ar;
这里面的 ar 怎么解释！ [/quote]

你是指在算法中的含义？
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