Deriving Max with fmincon when contraints differ

I am about to derive maximum values under linear contraint. Exactly describing

Target function is

 function f = utility(x) f = (0.7*x(1)^2 + 0.3*x(2)^2)^0.5

And then

 Aeq = [1 1] 
 beq = 100

So, using fmincon

 [x, fval] = fmincon(@utility, x0, [], [], Aeq, beq);

I actually derived the result.

HOWEVER, what I REALLY want to do is to change Aeq = [i 1] (i=1~10) and finally get a 10*3 matrix with i and x. Thru this, I could get a plot of x(:,2) against x(:,3).

So, I used FOR such as below. (I also changed initial guessing values X()

 ======================= 
Aeq = zeros(10,2); 
Aeq(:,1) = 1:1:10;Aeq(:,2)=1; 
X = zeros(10,2); 
X(:,1) = 100:-8:28;X(:,2)=100:-8:28;
 for i=1:10 beq = 100; 
 [x] = fmincon(@utility, X(i,:), [], [], Aeq(i,:), beq); 
 S = [Aeq(i) x];
 end

==========================

Result doesn't give me what i WANT. What is wrong with these lines?

Please, help me.

Thanks in advance.

Answer 1

[Andrew Newell]

If I understand your request, you want the matrix S to have two columns containing the values of Aeq and two columns containing the values of x(2) and x(3) for each case. This should do it:

f = @(x) (0.7*x(1)^2 + 0.3*x(2)^2)^0.5;
Aeq = ones(10,2); Aeq(:,1) = 1:10;
X = [100:-8:28; 100:-8:28]';
beq = 100;

options = optimset('fmincon');
options = optimset(options,'Algorithm','sqp');
S = [Aeq zeros(10,2)];
for i=1:10
    S(i,3:4) = fmincon(f, X(i,:), [], [], Aeq(i,:), beq, [], [], [], options);
end

The options settings eliminated some warnings.

[Joon Jeon]

It results some error such as followings.

??? Error using ==> optimset at 242

Invalid value for OPTIONS parameter Algorithm:

must be 'active-set', 'trust-region-reflective', 'interior-point',

'levenberg-marquardt', 'trust-region-dogleg', or 'lm-line-search'.

Error in ==> minmin at 7

options = optimset(options,'Algorithm','sqp');

I thought that 'Algorithm' should be substituted to one of the options in the warning message such as 'active-set'. So I tried but it still gives a error message

[Andrew Newell]

What version of MATLAB do you have? Try getting rid of the options.