How to use augmented Lagrange multipliers for inequality constrains to solve min max problem with iterations

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bassant tolba 2022-11-23

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https://ww2.mathworks.cn/matlabcentral/answers/1860613-how-to-use-augmented-lagrange-multipliers-for-inequality-constrains-to-solve-min-max-problem-with-it

编辑： Torsten 2022-11-23

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.

note that

subject to

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

lagrange_equation=sum(sum(equation));

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bassant tolba 2022-11-23

It’s obvious that anyone who are asking in Mathworks that they are not masters of MATLAB language and they need help for solving problems. Thus, Mathworks is established for sharing the knowledge and help each other not for refusing and considering a question as a trivial like you considered from your side. Anyway. Thanks!

Torsten 2022-11-23

编辑：Torsten 2022-11-23

...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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