[X,Y]= meshgrid(-4:.1:4);

Z=X.^2 + X.*Y + 0.5*Y.^2 - X - Y;

contour(X,Y,Z);

meshc(X,Y,Z);

zad18

tolfun=10^-5;

tolx=10^-3;

options=optimset('Tolx', tolx, 'TolFun',tolfun,'PlotFcns',@optimplotfval);

figure(1);

fun=@(x)sin(x(1)).*sin(x(2)).*exp(-(x(1).^2+x(2).^2));

x0=[-1,1];

%x0=[1,-1];

[x,fval,exitflag,output] = fminsearch(fun,x0,options)

figure(2);

[x,y]=meshgrid(-3:0.1:3, -3:0.1:3);

z=sin(x).*sin(y).*exp(-((x).^2+y.^2));

surf(x,y,z)

figure(3);

contourf(x,y,z);

zad1

tolx=10^-16;

tolfun=10^-8;

options=optimset('TolFun',tolfun,'PlotFcns',@optimplotfval);

fun = @(x) (x(1)-2)^2+(x(2)-2)^2;

x0=[5,3];

[x,fval,exitflag,output]=fminsearch(fun,x0,options)

zad3

clc;

clear;

[X,Y]= meshgrid(-4:.1:4);

Z=X.^2 + X.*Y + 0.5*Y.^2 - X - Y;

contour(X,Y,Z);

%meshc(X,Y,Z);

tolx=10^-6;

tolfun=10^-2;

options=optimset('TolFun',tolfun,'PlotFcns',@optimplotfval);

%fun = @(x) (x(1)-2)^2+(x(2)-2)^2;

fun = @(x) 4*x(1)^2-2.1*x(1)^4+(1/3)*x(1)^6+x(1)*x(2)-4*x(2)^2+4*x(2)^4

%fun = @(x) x(1)^2 + x(1)*x(2) + 0.5*x(2)^2 - x(1) - x(2);

x0=[0,0];

[x,fval,exitflag,output]=fminsearch(fun,x0,options)

zad 3

clc;

clear;

[X,Y] = meshgrid(-2:0.1:2, -1.2:0.1:1.2);

%Z=X.^2 + X.*Y + 0.5*Y.^2 - X - Y;

Z= 4*X.^2-2.1*X.^4+(1/3)*X.^6+X.*Y-4*Y.^2+4*Y.^4;

figure(1)

V = -3:0.1:2.5;

%V = -100:0.05:100;

[C,h] = contour(X,Y,Z,V);

set(h,'ShowText','on','TextStep',get(h,'LevelStep')*2)

%meshc(X,Y,Z);

%surf(X,Y,Z)

tolx=10^-8;

tolfun=10^-2;

options=optimset('TolX',tolx,'TolFun',tolfun,'PlotFcns',@optimplotfval);

fun = @(x) 4*x(1)^2-2.1*x(1)^4+(1/3)*x(1)^6+x(1)*x(2)-4*x(2)^2+4*x(2)^4;

%x0=[-1.5,-0.5];

%x0=[1.5,0.5];

x0=[0,1];

%x0=[0,-1];

%x0=[-1.5,0.9];

%x0=[1.5,-0.9];

%[x,fval,exitflag,output]=fminsearch(fun,x0,options)

[x,fval,exitflag,output, grad, hessian]=fminunc(fun,x0,options)

zad4

3. ogr liniowe

[x y]=meshgrid(-4:.1:4);

z=x.^2+x.*y+0.5.*y.^2-x-y;

con =-x+y+1;

con1 = x+y-4;

contour(x,y,z)

hold on

contour(x,y,con,[1e-8])

hold on

contour(x,y,con1,[1e-8])

tolfun=10^-1;

tolcon=10^-1;

options=optimset('TolFun', tolfun, 'TolCon',tolcon,'PlotFcns','optimplotfval', 'display' , 'iter');

fun = @(x)x(1).^2+x(1).*x(2)+0.5.*x(2).^2-x(1)-x(2);

x0=[2 -2];

A=[-1 1; 1 1];

b=[-1 ;4];

[x,fval,exitflag,output]=fmincon(fun,x0,A,b,[],[],[],[],[],options)

3.ogr nieliniowe

[x y]=meshgrid(-4:.1:4);

z=x.^2+x.*y+0.5.*y.^2-x-y;

con =-x+y+1;

con1 = x+y-4;

con2=y-x.^2;

contour(x,y,z)

hold on

contour(x,y,con2,[1e-8])

tolcon=10^-1;

options=optimset( 'TolCon',tolcon,'PlotFcns',@optimplotconstrviolation, 'display' , 'iter');

fun = @(x)x(1).^2+x(1).*x(2)+0.5.*x(2).^2-x(1)-x(2);

x0=[0.5 0.2];

[x,fval,exitlog,out] = fmincon(fun,x0,[],[],[],[],[],[],@(x) mycon(x),options)

Funkcja mycon.m

function [c,ceq] = mycon(x)

c=x(2)-x(1)^2;

ceq=[];

17.ogrniczenie liniowe

[x y]=meshgrid(0:.1:6,0:.1:6);

z=4*x.^2-2.1*x.^4+1/3*x.^6+x.*y-4*y.^2+4*y.^4;

con=-x-y+6

figure(2)

contour(x,y,z)

hold on

contour(x,y,con,[1e-8])

x0=[3.2 3.2];

x0=[3.2 3.2];

tolcon=10^-1;

options=optimset('TolCon',tolcon,'PlotFcns',@optimplotfval, 'display' , 'iter');

fun = @(x)4.*x(1).^2-2.1.*x(1).^4+(1/3).*x(1).^6+x(1).*x(2)-4.*x(2).^2+4.*x(2).^4;

[x,fval,exitlog,out] = fmincon(fun,x0,[],[],[],[],[],[],@(x) mycon1(x),options)

Funkcja mycon1.m

function [c,ceq] = mycon1(x)

c=-x(1)-x(2)+6;

ceq=[];

17organiczenie nieliniowe

[x y]=meshgrid(4:.1:6,4:.1:6);

z=4*x.^2-2.1*x.^4+1/3*x.^6+x.*y-4*y.^2+4*y.^4;

con=(x-5).^2+(y-5).^2-1;

figure(2)

contour(x,y,z)

hold on

contour(x,y,con,[1e-8])

x0=[5 5];

tolcon=10^-1;

options=optimset('TolCon',tolcon,'PlotFcns',@optimplotconstrviolation, 'display' , 'iter');

fun = @(x)4.*x(1).^2-2.1.*x(1).^4+(1/3).*x(1).^6+x(1).*x(2)-4.*x(2).^2+4.*x(2).^4;

[x,fval,exitlog,out] = fmincon(fun,x0,[],[],[],[],[],[],@(x) mycon2(x),options)

Funkcja mycon2.m

function [c,ceq] = mycon2(x)

c=(x(1)-5)^2+(x(2)-5)^2-1;

ceq=[];

jeśli chcesz wartości w iteracjach to zamieniasz @optimplotconstrviolation na @optimplotfval