how to plot a function subject to constraints in matlab

Question

I have this function:

function f=cost(x)
f=1.10471*x(1)^2*x(2)+0.04811*x(3)*x(4)*(14.0+x(2));

subject to

g(1)=tau-tau_max;
g(2)=sigma-sigma_max;
g(3)=x(1)-x(4);
g(4)=0.10471*x(1)^2+0.04811*x(3)*x(4)*(14+x(2))-5.0;
g(5)=0.125-x(1);
g(6)=delta-delta_max;
g(7)=P-PcX;

all g[1..7] should be <= 0

I have to keep any two of them as a constant and plot the f(x) The upper and lower bounds are respectively (x1..x4)

LowerBound=[0.125  0.1   0.1  0.125];
UpperBound=[5.0   10.0  10.0    5.0];    

thanks in advance...

edit: so far what i have done:

function [x1,x2,x3,x4]=objFuncPlot
[x2, x3] = meshgrid(0.1:.1:10, 0.1:.1:10);
//x1 and x4 is constant
x1=0.1996;
x4=0.2107;
//calculating constraints
[g1,g2,g3,g4,g5,g6,g7]=constraints(x1,x2,x3,x4); 
G1=[g1,g2,g4,g6,g7];
G2=[g3,g5];
infeasible=~all(G1(:)<=0) | ~all(G2(:)<=0);
//objective function
f=1.10471.*x1^2.*x2+0.04811.*x3.*x4.*(14.0+x2);
f(infeasible)=nan;
//plotting surf
surf(x2,x3,f,'LineStyle','none');
view(68,20)
hold on
xlabel('x');ylabel('y');zlabel('z');
hold off

//Constraints & Constants & Equations
function [g1,g2,g3,g4,g5,g6,g7]=constraints(x1,x2,x3,x4)
P=6000;
L=14;
E=30.*10^6;
G=12.*10^6;
tau_max=13600;
sigma_max=30000;
delta_max=0.25;
M=P*(14+x2./2);
R=sqrt(x2^2./4+(x1+x3)^2./4);
J=2.*(x1.*x2.*sqrt(2).*(x2^2/12+(x1+x3)^2/4));
tau_one=P./(sqrt(2).*x1.*x2);
tau_two=(M.*R)./J;
tau=sqrt(tau_one^2+2.*tau_one.*tau_two.*x2./(2.*R)+tau_two^2);
sigma=(6.*P.*L)./(x4.*x3^2);
delta=(4.*P.*L^3)./(30.*10^6.*x4.*x3^3);
PcX=4.013.*E./L^2.*sqrt(x3^2.*x4^6./36).*(1-x3.*sqrt(E./(4.*G))./(2.*L));
g1=tau-tau_max;
g2=sigma-sigma_max;
g3=x1-x4;
g4=0.10471.*x1^2+0.04811.*x3.*x4.*(14+x2)-5.0;
g5=0.125-x1;
g6=delta-delta_max;
g7=P-PcX;

Answer 1

A simple approach would be to define a new function which returns 1 when its argument is less than or equal to zero and returns NaN for +ve arguemnt

function H = mod_neg_step(argument)
         H = zeros(size(argument));
         H(argument<= 0) = 1;
         H(argument> 0) = NaN;
end

Then redefine your function f as

f=1.10471*x(1)^2*x(2)+0.04811*x(3)*x(4)*(14.0+x(2));
f=f*mod_neg_step(g(1))*mod_neg_step(g(2))*mod_neg_step(g(3))*mod_neg_step(g(4))...
  *mod_neg_step(g(5))*mod_neg_step(g(6))*mod_neg_step(g(7));

This will ensure that when g(1)...g(7) are positive your function f returns value NaN.Only when all of g(1)...g(7) are 0 or negative, function f will return

f=1.10471*x(1)^2*x(2)+0.04811*x(3)*x(4)*(14.0+x(2));