% Example 5.4
r=10; x0=[r 1];
for k=1:10
 x(k,:)=((r-1)/(r+1))^k*[r (-1)^k];
end
x = [x0; x];
figure(1);hold on; axis equal;
line(x(:,1),x(:,2),'marker','o')
%
x = linspace(-12,12);
y = linspace(-5,5);
[X,Y] = meshgrid(x,y);
Z = X.^2 + r*Y.^2;
contour(X,Y,Z,[0.1 0.5 1 2 5 10 20 30 50 70 100])
%-----------------------------------------------------------------------------
%
% Section 5.7
function f = objfun(x)
 f = exp(x(1))*(4*x(2)^2 + 2*x(2)^2 + 4*x(1)*b(2) + 2*x(2) + 1);
end
%
function [c, ceq] = confun(x)
% Nonlinear inequality constraint
 c = [1.5 + x(1)*x(2) – x(1) – x(2);
      -x(1)*x(2) – 10];
% Nonlinear equality constraints
 ceq = [];
end
%
x0 = [-1,1]; % Make a starting guess at the solution
options = optimset('LargeScale','off');
[x, fval, exitflag, output, lambda, grad, hessian] = ...
fmincon(@objfun,x0,[],[],[],[],[],[],@confun, options)
%-----------------------------------------------------------------------------
%
% Example 5.11
function f=quad2(x)
 global a
 f=x(1)^2+a*x(2)^2;
end
%
function [c,ceq]=ring(x)
 c(1)=10^2-x(1)^2-x(2)^2;
 c(2)=x(1)^2+x(2)^2-20^2;
 ceq=[];
end
%
global a
x0=[1,10];a=10;
[x,fval,exitflag,output,lambda]=fmincon(@quad2,x0,[],[],[],[],[],[],@ring)
%-----------------------------------------------------------------------------