approaching goal attaining optimization problem

I have a equation, I'm trying to aim for certrain fixed output but I have single equation and two variables to change. i'm trying achieve fixed sigma value. L0, t01 are optimized output values for fixed sigma values. I have no clue, how to approach this problem, I tried few things but they did't work out. Could someone help me with my problem? Thank you in advance.

%Below Rt and N are user defined
%T is fixed as well
% L0 upperbound 200 
%t01 upperbound 28

j = sym('j');
Area= eval((L0*t01*symsum((4^(j+1))*((0.5)^j)*(Rt^j),j,0,N-1))-((t01^2)*symsum(2^(2*j+1)*(Rt^((2*j)-1)),j,1,N-1))-((t01^2)*symsum(2^(2*j+2)*Rt^(2*j),j,0,N-1)));
Sigma= (Area/T^2)*100;

x0=[200 20];
A  = []; Aeq = []; Beq = [];  B=[];
options = optimoptions(@fmincon,'Algorithm','trust-region-reflective','TolFun',1e-14,'TolX',1e-14,'MaxFunEvals',10000,'MaxIter',10000,'Display','iter');
lb=[180 20]
ub=[200 28]
sigma
fun = @(L0,t01)(Sigma-(Area/T^2)*100);
[fval1,fval2]=fmincon(@fun,x0,A,B,Aeq,Beq,lb,ub,@confunc)

[Torsten]

What is N ?

What is Rt ?

Where is confunc ?

You set Sigma = Area/T^2 * 100 . So what does

fun = @(L0,t01)(Sigma-(Area/T^2)*100); 

mean - it's always =0 ?

Please describe in more detail what you try to do.

[Chandra Sekhar Kommineni]

N(no of iterations: 3) and Rt(0.4) are two user defined variables. I wrote a function to calculate Sigma using N,Rt, L0 and t01. but I'm working on specific problem where I need to fix sigma and find out L0, t01.

Sigma = Area/T^2 * 100, so here I want fix a value for sigma and find out L0 and t01 .

I'm sorry there is no confunc, I copied some code from online.

[Torsten]

So for given values of N, Rt and T you want to determine L0 and t01 such that Area/T^2*100 equals a prescribed value of sigma ?

[Chandra Sekhar Kommineni]

Yes, Exactly. Could you please explain how to appraoch the problem?

[Chandra Sekhar Kommineni]

I wrote below script, but it is not working. I'm receiving following error, Failure in initial objective function evaluation. Optimization cannot continue.

goal=33;
weight=0.2;
x0=[150 10 0.3];
lb=[150 10 0.3];
ub=[220 30 0.5];

x = fgoalattain(@myfun,x0,goal,weight,[],[],[],[],lb,ub);

function Sigma= myfun(L0,t01,Rt)
T=320;
N=3;
 j = sym('j');
Area= eval((L0*t01*symsum((4^(j+1))*((0.5)^j)*(Rt^j),j,0,N-1))-((t01^2)*symsum(2^(2*j+1)*(Rt^((2*j)-1)),j,1,N-1))-((t01^2)*symsum(2^(2*j+2)*Rt^(2*j),j,0,N-1)));
Sigma= (Area/T^2)*100;

end

[Torsten]

x = fgoalattain(@(x)myfun(x(1),x(2),x(3)),x0,goal,weight,[],[],[],[],lb,ub);

[Chandra Sekhar Kommineni]

Thank you for your help, but I'm getting wrong results. I'm getting lb values as output

[Torsten]

And you are sure that the problem you formulated is really what you want to solve ? Because you said Rt is also given - now it turns out that it is a solution variable, too. And you said you prescribe a sigma and try to adjust L0 and t01 such that Area/T^2 * 100 approximates sigma best possible. But where is this sigma in your problem formulation ?

What you now try to solve is

min: gamma

such that

Area/T^2 * 100 - gamma*0.2 <= 33

something quite different, I guess.

[Chandra Sekhar Kommineni]

I wanted tried with Rt also variable.

can you please explain what is this ? Area/T^2 * 100 - gamma*0.2 <= 33 ?

[Chandra Sekhar Kommineni]

i tried using fmicon, but similar results(output as lower bound values, I'm getting fval negative). I don't know, I'm missing something.

x0=[1 1  0.1];
lb=[ 150 10 0.1];
ub=[210 30 0.5];

[x,fval] = fmincon(@ (x) myfun (x (1), x (2), x (3)),x0,[],[],[],[],lb,ub);

function Sigma= myfun(L0,t01,Rt)
T=320;
N=2;
 j = sym('j');
Area= ((L0*t01*symsum((4^(j+1))*((0.5)^j)*(Rt^j),j,0,N-1))-((t01^2)*symsum(2^(2*j+1)*(Rt^((2*j)-1)),j,1,N-1))-((t01^2)*symsum(2^(2*j+2)*Rt^(2*j),j,0,N-1)));

%Sigma=double((Area/T^2))*100
Sigma= double(Area/T^2 * 100) -33; 
end

[Chandra Sekhar Kommineni]

I did tweaks to the above code, somewhat I achieved the goal. I added "options" to fgoalattain, its working sometimes, sometimes error is more. Can you please tell whats happening in optimset? is there anything else to improve the code

clc;clear all;
goal=29;
weight=0.0001;
x0=[1.0 1.0 0.1];
lb=[204 18 0.4];
ub=[230 26 0.48];
options = optimset( 'Display' , 'iter' , ...
    'GoalsExactAchieve' ,2);
%options = optimoptions(@lsqnonlin,'Algorithm','trust-region-reflective','TolFun',1e-14,'TolX',1e-14,'MaxFunEvals',10000,'MaxIter',10000,'Display','iter');

 [x, feval]= fgoalattain(@ (x) myfun (x(1), x(2), x(3)), x0, goal, weight, [], [], [], [],lb,ub,[],options);