## Documentation Center |

Find values of *x* that minimize

*f*(*x*) = (*x*_{1} –
0.2)^{2} + (*x*_{2}–
0.2)^{2} + (*x*_{3}–
0.2)^{2},

where

for all values of *w*_{1} and *w*_{2} over
the ranges

1 ≤ *w*_{1} ≤
100,

1 ≤ *w*_{2} ≤
100,

starting at the point *x* = [0.25,0.25,0.25].

Note that the semi-infinite constraint is two-dimensional, that is, a matrix.

First, write a file that computes the objective function.

function f = myfun(x,s) % Objective function f = sum((x-0.2).^2);

Second, write a file for the constraints, called `mycon.m`.
Include code to draw the surface plot of the semi-infinite constraint
each time `mycon` is called. This enables you to
see how the constraint changes as `X` is being minimized.

function [c,ceq,K1,s] = mycon(X,s) % Initial sampling interval if isnan(s(1,1)), s = [2 2]; end % Sampling set w1x = 1:s(1,1):100; w1y = 1:s(1,2):100; [wx,wy] = meshgrid(w1x,w1y); % Semi-infinite constraint K1 = sin(wx*X(1)).*cos(wx*X(2))-1/1000*(wx-50).^2 -... sin(wx*X(3))-X(3)+sin(wy*X(2)).*cos(wx*X(1))-... 1/1000*(wy-50).^2-sin(wy*X(3))-X(3)-1.5; % No finite nonlinear constraints c = []; ceq=[]; % Mesh plot m = surf(wx,wy,K1,'edgecolor','none','facecolor','interp'); camlight headlight title('Semi-infinite constraint') drawnow

Next, invoke an optimization routine.

x0 = [0.25, 0.25, 0.25]; % Starting guess [x,fval] = fseminf(@myfun,x0,1,@mycon)

After nine iterations, the solution is

x x = 0.2522 0.1714 0.1936

and the function value at the solution is

fval fval = 0.0036

The goal was to minimize the objective *f*(*x*)
such that the semi-infinite constraint satisfied *K*_{1}(*x*,*w*) ≤ 1.5. Evaluating `mycon` at
the solution `x` and looking at the maximum element
of the matrix `K1` shows the constraint is easily
satisfied.

[c,ceq,K1] = mycon(x,[0.5,0.5]); % Sampling interval 0.5 max(max(K1)) ans = -0.0333

This call to `mycon` produces the following
surf plot, which shows the semi-infinite constraint at `x`.

Was this topic helpful?