How use fmincon for a function with many variables?

I should minimize this function but don't know how please help me.

cost function:

([31.4*(R0^2- R1^2) *H1 ] + [ 24.7* R2^2*H2]) +u1(-10.856*(R0^2-R1^2)+2400+S1^2) + u2(10.856*(R0^2-R1^2)-2950+S2^2) + u3(-R0 + S3^2) + u4(R0 -17+ S4^2) + u5(-R1 + S5^2) + u6(R1 -13.3+ S6^2) + u7(-R2 + S7^2) + u8(R2 -24.6+ S8^2) + u9(-H1 + S9^2) + u10(H1-32+ S10^2) + u11(-H2 + S11^2) + u12(H1 -69.8+ S12^2).

constraints :

1: u4 - u3 - (2714*R0*u1)/125 + (2714*R0*u2)/125 + (314*H1*R0)/5=0

2:u6 - u5 + (2714*R1*u1)/125 - (2714*R1*u2)/125 - (314*H1*R1)/5=

3:u8 - u7 + (247*H2*R2)/5=0

4:(157*R0^2)/5 - u9 + u10 + u12 - (157*R1^2)/5 =0

5:(247*R2^2)/10 - u11=0

1357*R1^2)/125 + S1^2 - (1357*R0^2)/125 + 2400=0

1357*R0^2)/125 + S2^2 - (1357*R1^2)/125 – 2950=0

S3^2 - R0=0

S4^2 + R0 – 17=0

S5^2 - R1=0

S6^2 + R1 - 133/10 =0

S7^2 - R2=0

S8^2 + R2 - 123/5= 0

S9^2 – H1=0

S10^2 + H1 – 32=0

S11^2 - H2=0

S12^2 + H1 - 349/5=0

ui * sj=0. i= 0 to 12.

j= 0 to 12.

Thanks in advance

Answer 1

[Ayush Modi]

Hi Reihaneh,

I understand you want to minimize the given cost function using "fmincon" variable but having difficulty due to multiple parameters. You can pass them as an array in the function parameters. Here is the example code to get you started:

function example(vars)
    a = vars(1);
    b = vars(2);
    ... your logic...
end

% To call the fmincon
fmincon(@(x) example(x,n), initial_guess, ...other arguments...)
    
% Here, vars is an array of variables

Refer to the following MathWorks documentation to know how to pass extra or fixed parameters:

https://www.mathworks.com/help/optim/ug/passing-extra-parameters.html