Parallel optimization with extra parameters (fmincon)

how do i run optimization (fmincon) repeatedly

I have a function

f = p1 + 2*a*c*p2 + 2*a*b*p3 + 2*b*c*p4

where

p1=-sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)+((x(6)-x(5))/2))+sin(((x(4)-x(3))/2)+((x(6)-x(5))/2)-((x(2)-x(1))/2))+sin(((x(2)-x(1))/2)+((x(6)-x(5))/2)-((x(4)-x(3))/2))+sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)-((x(6)-x(5))/2));

p2=sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)+((x(6)-x(5))/2))+sin(((x(4)-x(3))/2)+((x(6)-x(5))/2)-((x(2)-x(1))/2))-sin(((x(2)-x(1))/2)+((x(6)-x(5))/2)-((x(4)-x(3))/2))+sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)-((x(6)-x(5))/2));

p3=sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)+((x(6)-x(5))/2))-sin(((x(4)-x(3))/2)+((x(6)-x(5))/2)-((x(2)-x(1))/2))+sin(((x(2)-x(1))/2)+((x(6)-x(5))/2)-((x(4)-x(3))/2))+sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)-((x(6)-x(5))/2));

p4=sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)+((x(6)-x(5))/2))+sin(((x(4)-x(3))/2)+((x(6)-x(5))/2)-((x(2)-x(1))/2))+sin(((x(2)-x(1))/2)+((x(6)-x(5))/2)-((x(4)-x(3))/2))-sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)-((x(6)-x(5))/2));

and x1 until x6 are angles subject to the bound constraint from 0 to pi.

I want to minimize this function for a range of a=[0:0.01:1] and b=[0:0.01:1]. (That is, I want to minimize this function for each a,b=0, a,b=0.01,a,b=0.02 ... and so on). *Also , there is a normalize condition which is a^2+b^2+c^2=1.*

so this my code

Step 1: Write a file objfun.m.

function f= objfun (x,a,b,c)

a=.57;

b=.57;    % i pick a number for a,b

c=sqrt(1-a*a-b*b);
p1=-sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)+((x(6)-x(5))/2))+sin(((x(4)-x(3))/2)+((x(6)-x(5))/2)-((x(2)-x(1))/2))+sin(((x(2)-x(1))/2)+((x(6)-x(5))/2)-((x(4)-x(3))/2))+sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)-((x(6)-x(5))/2));
p2=sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)+((x(6)-x(5))/2))+sin(((x(4)-x(3))/2)+((x(6)-x(5))/2)-((x(2)-x(1))/2))-sin(((x(2)-x(1))/2)+((x(6)-x(5))/2)-((x(4)-x(3))/2))+sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)-((x(6)-x(5))/2));
p3=sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)+((x(6)-x(5))/2))-sin(((x(4)-x(3))/2)+((x(6)-x(5))/2)-((x(2)-x(1))/2))+sin(((x(2)-x(1))/2)+((x(6)-x(5))/2)-((x(4)-x(3))/2))+sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)-((x(6)-x(5))/2));
p4=sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)+((x(6)-x(5))/2))+sin(((x(4)-x(3))/2)+((x(6)-x(5))/2)-((x(2)-x(1))/2))+sin(((x(2)-x(1))/2)+((x(6)-x(5))/2)-((x(4)-x(3))/2))-sin(((x(2)-x(1))/2)+((x(4)-x(3))/2)-((x(6)-x(5))/2));
%f=4*(p1+C13*p2+C12*p3+C23*p4);
f=p1+2*a*c*p2+2*a*b*p3+2*b*c*p4;

Step 2: Invoke constrained optimization routine.

x=[x(1),x(2),x(3),x(4),x(5),x(6)]; % angles;
lb=[0,0,0,0,0,0];
ub=[pi,pi,pi,pi,pi,pi];
x0=[pi/8;pi/3;0.7*pi;pi/2;.5;pi/4];
[x,fval]=fmincon(@objfun,x0,[],[],[],[],lb,ub)

the solution produced is

x=

2.5530

0.6431

2.5305

0.6195

2.5531

0.6421

fval=

-4.3546

can any one change the code so that, the optimization will run for 0:0.01:1 times, and save the optimal values for each a,b?

Answer 1

[Marc]

You can try a for loop...

Something like this.

a = 0:0.01:1;
b = 0:0.01:1;

mSize = max(size(a));

xNew = zeros(mSize,6); % Preallocate for speed
fNew = zeros(mSize,1);

for n = 1:mSize
    a1 = a(n);
    b1 = b(n);
    %%%here you put your c and fmincon like above

      xNew(n,:) = x; % from fmincon
      fNew(n) = feval; % from fmincon
  end

I think this should work. May take a while. You may want to start with something like a = 0:0.1:1 before trying the rest.

The code above assumes a and b will always be equal. If you want different combinations, then you will need two for loops. One nested within.

[Raja Emlik]

Thanks for your replay . In the problem there a normalize condition which is a^2+b^2+c^2=1 so i need to put if statement as well. could you please help me for different combinations, actually i did many code for that but it could not work as i have not used matlab. Thanks in advance.