Безусловная многомерная оптимизация

xt-align:justify">void regul_simplex()

{

double *px_1,*px_2,*py;

double eps,min,l1,max,l2,r,c1,c2,u1,u2,X1,X2,Y,y;

int i,N,N1,L1,L2;

N1=1;

px_1=new double[3];

px_2=new double[3];

py=new double[3];

cout<<"Vvedite bazovuyu tochku:/n"<<endl;

cout<<"x0(x1,x2) ";cout<<endl;

cout<<"x1 = "; cin>>px_1[0];

cout<<"x2 = "; cin>>px_2[0];

cout<<"eps = "; cin>>eps;

cout<<"r = "; cin>>r;

px_1[1]=px_1[0]+r;

px_2[1]=px_2[0];

px_1[2]=px_1[0];

px_2[2]=px_2[0]+r;

py[0]=25*px_1[0]+0.9*px_2[0]+exp(0.35*(px_1[0]*px_1[0]+px_2[0]*px_2[0]));

py[1]=25*px_1[1]+0.9*px_2[1]+exp(0.35*(px_1[1]*px_1[1]+px_2[1]*px_2[1]));

py[2]=25*px_1[2]+0.9*px_2[2]+exp(0.35*(px_1[2]*px_1[2]+px_2[2]*px_2[2]));

N=3;

point1:

min=py[0]; l1=0;

for(i=1;i<=2;i++)

{if(py[i]<min)

  {min=py[i];

   l1=i;

  }

}

max=py[0]; l2=0;

for(i=1;i<=2;i++)

{if(py[i]>max)

  {max=py[i];

   l2=i;

  }

}

if(r>eps)

{c1=0; c2=0;

for(i=0;i<=2;i++)

{if(i==l2) continue;

c1=c1+px_1[i];

c2=c2+px_2[i];

}

L2=l2;

L1=l1;

u1=c1-px_1[L2];

u2=c2-px_2[L2];

y=25*u1+0.9*u2+exp(0.35*(u1*u1+u2*u2));

N++;

if(y<py[L2])

{px_1[L2]=u1;

px_2[L2]=u2;

py[L2]=y;

}

else

{for(i=0;i<=2;i++)

{if(i==L1) continue;

  px_1[i]=(px_1[i]+px_1[L1])*0.5;

  px_2[i]=(px_2[i]+px_2[L1])*0.5;

  py[i]=25*px_1[i]+0.9*px_2[i]+exp(0.35*(px_1[i]*px_1[i]+px_2[i]*px_2[i]));

  N++;

}

  r=r*0.5;

 

}

cout<<px_1[L1]<<" "<<px_2[L1]<<endl;

N1++;

 

goto point1;

}

X1=px_1[L1];

X2=px_2[L1];

Y=25*px_1[L1]+0.9*px_2[L1]+exp(0.35*(px_1[L1]*px_1[L1]+px_2[L1]*px_2[L1]));

cout<<"x_(x1,x2) = x_( "<<X1<<","<<X2<<" )"<<endl;

cout<<"y_ = "<<Y<<endl;

cout<<"Kol-vo icpitanii: N = "<<N<<endl;

cout<<"Kol-vo iteracii N1="<<N1<<endl;

 

}

 

 

 

void grad_s_drobl()

{const int L=1500;

znach_x x[L];

znach_x x_;

double a,eps,delta,z1,z2,y,y1,d,y_;

int k,N,N1,N0;

cout<<"Vvedite bazovuyu tochku:/n"<<endl;

cout<<"x0(x1,x2) ";cout<<endl;

cout<<"x1 = ";

cin>>x[0].x1;

cout<<"x2 = ";

cin>>x[0].x2;

cout<<"Vvedite a:\n";

cout<<"a = ";cin>>a;

cout<<"Vvedite tochnost':\n";

cout<<"eps = "; cin>>eps;

cout<<"Vvedite delta:\n";

cout<<"delta = "; cin>>delta;

k=0;

z1=25+0.7*x[0].x1*exp(0.35*(pow(x[0].x1,2)+pow(x[0].x2,2)));

z2=0.9+0.7*x[0].x2*exp(0.35*(pow(x[0].x1,2)+pow(x[0].x2,2)));

 

N1=2;N0=0;

d=sqrt(pow(z1,2)+pow(z2,2));

 

m2:

y=25*x[k].x1+0.9*x[k].x2+exp(0.35*(pow(x[k].x1,2)+pow(x[k].x2,2)));

 

N0++;

m1:

y1=25*(x[k].x1-a*z1)+0.9*(x[k].x2-a*z2)+exp(0.35*(pow((x[k].x1-a*z1),2)+pow((x[k].x2-a*z2),2)));

 

if ((y1-y)>(-a*delta*d)) {a=a/2.0;

  goto m1;}

x[k+1].x1=x[k].x1-a*z1;

x[k+1].x2=x[k].x2-a*z2;

 

cout<<k<<" "<<x[k+1].x1<<" "<<x[k+1].x2<<endl;

cout<<endl;

 

z1=25+0.7*x[k+1].x1*exp(0.35*(pow(x[k+1].x1,2)+pow(x[k+1].x2,2)));

z2=0.9+0.7*x[k+1].x2*exp(0.35*(pow(x[k+1].x1,2)+pow(x[k+1].x2,2)));

N1=N1+2;

d=pow(z1,2)+pow(z2,2);

if (sqrt(d)>eps) {k=k+1;goto m2;}

    else{ x_=x[k+1];

y_=25*x_.x1+0.9*x_.x2+exp(0.35*(pow(x_.x1,2)+pow(x_.x2,2)));

N=N1+N0;}

 

cout<<"Result:\n";

cout<<"x_(x1,x2) = x_( "<<x_.x1<<","<<x_.x2<<" )"<<endl;

cout<<"y_ = "<<y_<<endl;

cout<<"Kol-vo icpitanii: N1 = "<<N1<<endl;

cout<<"Kol-vo icpitanii: N0 = "<<N0<<endl;

cout<<"Kol-vo icpitanii: N = "<<N<<endl;

cout<<"Kol-vo iteracii: k = "<<k<<endl;

}

 

void naisk_spusk()

{const int L=1500;

znach_x x[L];

znach_x x_;

double a,a1,a2,f1,f2,amin,eps,z1,z2,y1,d,y_,A,B,da,y2;

int k,i,N1,N,N0;

cout<<"Vvedite bazovuyu tochku:/n"<<endl;

cout<<"x0(x1,x2) ";cout<<endl;

cout<<"x1 = ";

cin>>x[0].x1;

cout<<"x2 = ";

cin>>x[0].x2;

cout<<"Vvedite tochnost':\n";

cout<<"eps = "; cin>>eps;

cout<<"Vvedite da:\n";

cout<<"da = "; cin>>da;

k=0;

N0=0;

z1=25+0.7*x[0].x1*exp(0.35*(pow(x[0].x1,2)+pow(x[0].x2,2)));

z2=0.9+0.7*x[0].x2*exp(0.35*(pow(x[0].x1,2)+pow(x[0].x2,2)));

N1=2;

m2:

 

y1=25*x[k].x1+0.9*x[k].x2+exp(0.35*(pow(x[k].x1,2)+pow(x[k].x2,2)));

//cout<<"y1= "<<y1<<endl;

i=0;

m1:

y2=25*(x[k].x1-((i+1)*da)*z1)+0.9*(x[k].x2-((i+1)*da)*z2)+exp(0.35*(pow((x[k].x1-((i+1)*da)*z1),2)+pow((x[k].x2-((i+1)*da)*z2),2)));

//cout<<"y2= "<<y2<<endl;

N0++;

if (y2<y1) {i++;y1=y2;goto m1;}

   else {B=(1+i)*da;

  if (i>0) A=(i-1)*da;

       else A=0;

  }

//cout<<"A="<<A<<" B="<<B<<endl;

 

//dich

d=eps/100;

 

do

   {a=(A+B)/2.0;

    a1=a-d;

    a2=a+d;

    f1=25*(x[k].x1-a1*z1)+0.9*(x[k].x2-a1*z2)+exp(0.35*(pow((x[k].x1-a1*z1),2)+pow((x[k].x2-a1*z2),2)));

    f2=25*(x[k].x1-a2*z1)+0.9*(x[k].x2-a2*z2)+exp(0.35*(pow((x[k].x1-a2*z1),2)+pow((x[k].x2-a2*z2),2)));

    N=0;

    N=N+2;

    cout<<"a1 = "<<a1<<" f1 = "<<f1<<endl;

    cout<<"a2 = "<<a2<<" f2 = "<<f2<<endl;

    if (f1<f2) B=a2;

       else A=a1;

    }

   while (B-A>2*eps);

 

amin=(A+B)/2.0;

 

// cout<<endl;

 

//cout<<"Result:  "<<"amin= "<<amin<<endl;

 

x[k+1].x1=x[k].x1-amin*z1;

x[k+1].x2=x[k].x2-amin*z2;

z1=25+0.7*x[k+1].x1*exp(0.35*(pow(x[k+1].x1,2)+pow(x[k+1].x2,2)));

z2=0.9+0.7*x[k+1].x2*exp(0.35*(pow(x[k+1].x1,2)+pow(x[k+1].x2,2)));

N1=N1+2;

if ((sqrt(z1*z1+z2*z2))>eps) {k=k+1; goto m2;}

    else {x_=x[k+1];

  y_=25*x_.x1+0.9*x_.x2+exp(0.35*(pow(x_.x1,2)+pow(x_.x2,2)));

N=N1+N0;

}

 

 

cout<<"Result:\n";

cout<<"x_(x1,x2) = x_( "<<x_.x1<<","<<x_.x2<<" )"<<endl;

cout<<"y_ = "<<y_<<endl;

cout<<"Kol-vo icpitanii: N1 = "<<N1<<endl;

cout<<"Kol-vo icpitanii: N0 = "<<N0<<endl;

cout<<"Kol-vo icpitanii: N = "<<N<<endl;

cout<<"Kol-vo iteracii: k = "<<k<<endl;

 

}

 

 

void evristich()

{

const int L=1500;

znach_x x[L];

znach_x x_;

double a1,a2,d1,d2,g1,g2,b1,b2,s1,s2;

double eps,y_,p1,p1_1,p2,p2_2,norma;

int k;

int N0=0,N1=0,N;

cout<<"Vvedite bazovuyu tochku:"<<endl;

cout<<"x0(x1,x2) ";cout<<endl;

cout<<"x1 = ";

cin>>x[0].x1;

cout<<"x2 = ";

cin>>x[0].x2;

cout<<"Vvedite tochnost':\n";

cout<<"eps = ";

cin>>eps;

a1=0.5;

a2=2;

d1=0.01;

d2=3;

k=0;

//N=0;N0=0;N1=0;

m1:

p1=dfx1(x[k].x1,x[k].x2);

p2=dfx2(x[k].x1,x[k].x2);

N1=N1+2;                   //N1-kol-vo vichislenii proizv.

if (abs(p1)>d1) g1=p1;

if (p1<=d1)   g1=0;

if (abs(p2)>d1) g2=p2;

if (p2<=d1) g2=0;

 

 

x[k+1].x1=x[k].x1-a1*g1;

x[k+1].x2=x[k].x2-a1*g2;

N0=N0+2;                  //N0 kol-vo vichislenii f

if (f(x[k+1].x1,x[k+1].x2)<f(x[k].x1,x[k].x2)) {k++;goto m1;}

m2:

p1_1=dfx1(x[k].x1,x[k].x2);

p2_2=dfx2(x[k].x1,x[k].x2);

N1=N1+2;

if (abs(p1)>d2) b1=0;

if (p1<=d2)   b1=p1_1;

if (abs(p2)>d2) b2=0;

if (p2<=d2) b2=p2_2;

 

x[k+1].x1=x[k].x1-a2*b1;

x[k+1].x2=x[k].x2-a2*b2;

N0=N0+2;

if (f(x[k+1].x1,x[k+1].x2)<f(x[k].x1,x[k].x2)) {k++;goto m2;}

 

s1=dfx1(x[k+1].x1,x[k+1].x2);

s2=dfx2(x[k+1].x1,x[k+1].x2);

N1=N1+2;

norma=sqrt(pow(s1,2)+pow(s2,2));

 

if (norma>eps)  {a1=0.5*a1;

a2=0.5*a2;

goto m1;}

N=N0+N1;

x_=x[k+1];

y_=f(x_.x1,x_.x2);

 

cout<<"Result:\n";

cout<<"x_(x1,x2) = x_( "<<x_.x1<<","<<x_.x2<<" )"<<endl;

cout<<"y_ = "<<y_<<endl;

cout<<"Kol-vo icpitanii: N1 = "<<N1<<endl;

cout<<"Kol-vo icpitanii: N0 = "<<N0<<endl;

cout<<"Itogo kol-vo icpitanii: N = "<<N<<endl;

cout<<"kol-vo iteracii k="<<k<<endl;

 

}

 

double ZS(double a,double b,double x1k,double x2k,double z1,int n)

{ double e0,t,x1,x2,fi1,fi2;

e0=0.0001;

t=(1+sqrt(5))/2;

 

x1=a+(b-a)/(t*t);

x2=a+(b-a)/t;

if (n==1)

{ fi1=f(x1k-x1*z1,x2k);

fi2=f(x1k-x2*z1,x2k);

do

{ if (fi1<fi2) { b=x2; x2=x1; fi2=fi1;

x1=a+b-x2;fi1=f(x1k-x1*z1,x2k); }

        else { a=x1; x1=x2; fi1=fi2;

x2=a+b-x1; fi2=f(x1k-x2*z1,x2k); }

}

while((b-a)/2>e0);

if (fi1<fi2) b=x2;

else   a=x1; }

else

{ fi1=f(x1k,x2k-x1*z1);

fi2=f(x1k,x2k-x2*z1);

do

{ if (fi1<fi2) { b=x2; x2=x1; fi2=fi1;

x1=a+b-x2; fi1=f(x1k,x2k-x1*z1); }

else { a=x1; x1=x2;fi1=fi2;

x2=a+b-x1; fi2=f(x1k,x2k-x2*z1); }

}

while((b-a)/2>e0);

if (fi1<fi2) b=x2;

else   a=x1; }

return ((a+b)/2); }

 

void gauss_zeidel()

{

int k,m;

double x1[100],x2[100];

double e2,dalpha;

double alphamin1,alphamin2,z1,z2,y1,y2,a1,b1,a2,b2,xmin1,xmin2,ymin,d;

k=0;

x1[0]=1;

x2[0]=0;

e2=0.0004;

dalpha=0.9;

cout<<setw(5)<<setiosflags(ios::left)<<"k"<<setw(14)<<"x1"<<setw(14)<<"x2"<<endl;

metka:

z1=dfx1(x1[2*k],x2[2*k]);

m=0;

y1=f(x1[2*k]-m*dalpha*z1,x2[2*k]);

metka1:

y2=f(x1[2*k]-(m+1)*dalpha*z1,x2[2*k]);

if (y2<y1)

{m++;y1=y2;goto metka1;}

else

{b1=(m+1)*dalpha;

if (m==0) a1=0;

else a1=(m-1)*dalpha; }

 

alphamin1=ZS(a1,b1,x1[2*k],x2[2*k],z1,1);

 

x1[2*k+1]=x1[2*k]-alphamin1*z1;

x2[2*k+1]=x2[2*k];

cout<<setw(5)<<setiosflags(ios::left)<<(k+1)<<setw(14)<<x1[2*k+1]<<setw(14)<<x2[2*k+1]<<endl;

 

z2=dfx2(x1[2*k+1],x2[2*k+1]);

m=0;

y1=f(x1[2*k+1],x2[2*k+1]-m*dalpha*z2);

metka2:

y2=f(x1[2*k+1],x2[2*k+1]-(m+1)*dalpha*z2);

if (y2<y1)

{m++;y1=y2;goto metka2;}

else

{b2=(m+1)*dalpha;

if (m==0) a2=0;

else a2=(m-1)*dalpha; }

 

alphamin2=ZS(a2,b2,x1[2*k+1],x2[2*k+1],z2,2);

 

x1[2*k+2]=x1[2*k+1];

x2[2*k+2]=x2[2*k+1]-alphamin2*z2;

cout<<setw(5)<<setiosflags(ios::left)<<" "<<setw(14)<<x1[2*k+2]<<setw(14)<<x2[2*k+2]<<endl;

 

d=sqrt(pow((x1[2*k+2]-x1[2*k]),2)+pow((x2[2*k+2]-x2[2*k]),2));

if (d>e2)

{k++;goto metka;}

else

{ xmin1=x1[2*k+2];

xmin2=x2[2*k+2];

ymin=f(xmin1,xmin2); }

cout<<endl<<endl;

cout<<"x1="<<xmin1<<", x2="<<xmin2<<"; y="<<ymin<<endl;

cout<<"N="<<(N0+N1)<<endl;

cout<<"k="<<(k+1)<<endl;

 

}

 

void main()

{int j;

 

while (true)

 

{clrscr();

 

cout<<endl;

cout<<"1.Poisk po obrazcu\n";

cout<<"2.Diformir. simpleks\n";