How to use augmented Lagrange multipliers for inequality constrains to solve min max problem with iterations
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Dear all,
I have this lagrange equation with some inequalities constrains. I want to apply augmented Lagrange multipliers for inequality constrains to solve min max problem and get the optimized values of the lagrange multipliers(k_and v_) and the remaining variables if its possible
Please can anyone help me ?
I apprecitae your help.
Here is my code for the lagrange equation and constraints.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1204453/image.png)
note that
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1204458/image.png)
subject to
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1204463/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1204468/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1204473/image.png)
here is my code of the equation and constraints.
TN=10;
expo=1;
pL=zeros(1,TN);
for l=1:TN
pL(l)=l^-expo;
end
beta=pL./sum(pL);
meu=pL./sum(pL);
zm=rand(1,10);
ro=rand(10,10); %
x=zm*ro;
CMRN=0.4*(10^5);
aa = 0.1;
bb = 1;
Fkf= ((bb-aa).*rand(10,1) + aa)*(10^9);
Rk=1.0e+08 *[ 3.0346, 4.2479,5.8977,5.7046, 6.1621,5.8498,5.7329,6.0979, 5.8282,6.2186];
a = 500;
b = 2000;
Lks = ((b-a).*rand(10) + a);
CK=[500,600,700,800,900,1000,1100,1200,1300,1400];
ls=[20000,20000,20000,20000,20000,20000,20000,20000,20000,20000];
for k=1:10
for s=1:10
(zm(s)*ls(s))<=CMRN; % the constraint (11f)
equation(k,s)=beta(k)*((Lks(k,s)*meu(s))/Rk(k)+(CK(k)*Lks(k,s)*meu(s))/Fkf(k))*x(k,s)+beta(k)*((Lks(k,s)*meu(s))/Rk(k)+(CK(k)*Lks(k,s)*meu(s))/Fkf(k))*(1-zm(s))+k_*(x(k,s)-zm(s))+v_*(x(k,s)-ro(k,s))
end
end
lagrange_equation=sum(sum(equation));
9 Comments
Torsten
on 23 Nov 2022
Edited: Torsten
on 23 Nov 2022
...considering a question as a trivial like you considered from your side.
At the contrary: I consider your question as much too difficult for me to answer since I still don't understand the model and I don't have the necessary background knowledge for coding it. So I had to invest a large amount of time that I'm not willing to spend on this. Your questions don't mainly address MATLAB skills, but understanding of the underlying subject. What I answered so far were just guesses on how I understood some passages of the article.
And besides this, all participants in this forum are volunteers - so you can ask for help, but voluntary help has limits.
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