File:Opti conti constrained.svg

function Opti_conti_constrained
clc
h = figure;
hold on;
grid on;
box on;
axis equal;
axis([0 2.5 0 4]+0.05*[-1 1 -1 1]);
x = 4/9:0.01:2;
hp = plot(x,sqrt(18-4.5*x),...
          [0.5 2],2*[0.5 2]-1,...
          [0 4/9],4*[1 1],...
          [0 0],[0 4],[0 0.5],[0 0]);
set(hp,'color',[0 0 0],'LineWidth',2)
[X,Y] = meshgrid(0:0.025:2.5,0:0.04:4);
Z = (X-1.5).^2+(Y-4).^2;
contour(X,Y,Z,50);
 
x0  = [0 0];
A   = [];
b   = [];
Aeq = [];
beq = [];
lb  = [];
ub  = [];
 
options = optimset('Display','iter','LargeScale','off',...
                   'GradObj','on',...
                   'Jacobian','off','Hessian','on',...
                   'TolX',1e-4,'TolFun',1e-4,'TolCon',1e-5,...
                   'MaxIter',1000,'MaxFunEvals',1e12);
 
[Sol_cons f_cons] = fmincon(@(x) myfun(x),x0,A,b,Aeq,beq,lb,ub,...
                            @(x) constraints(x),options);
 
[Sol_uncons f_uncons] = fminsearch(@(x)(x(1)-1.5)^2+(x(2)-4)^2,[0 0]);				   
 
plot(Sol_cons(1),Sol_cons(2),'ro')
plot(Sol_uncons(1),Sol_uncons(2),'r.')
colorbar
 
function [f,g,H] = myfun(x)
f = (x(1)-1.5)^2+(x(2)-4)^2;     % Compute the objective function value at x
if nargout > 1                   % fun called with two output arguments
   g = [2*x(1)-3;2*x(2)-8];      % Gradient of the function evaluated at x
   if nargout > 2
      H = [2 0;0 2];             % Hessian evaluated at x
   end
end
 
function [c,ceq] = constraints(x)
c(1,1) = 4.5*x(1)+x(2)^2-18;
 
A = [1 0;0 1;-1 0;0 -1;-2 1];
b = [4;4;0;0;1];
 
c(2:6,1) = A*x'-b;
ceq = [];