Minimalization problem LinearConstraint and conjugate gradient optimizer

2022 9 25
3 个回答
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更新时间：2022 9 30
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Problem, input data and equations are described in details in attachment. This matrix is called Ms in the below mentioned equation.
The equation is the function F(ω). Omega (ω) are the seven wages which I’m looking for by minimize values of the second equation. The condition is that ω1 + ω2 + ω3 + ω4 + ω5 + ω6 + ω7 = 1.
When using Scipy.stats, the LinearConstraint and Conjugate gradient optimizer were used.
The obtained results were: 0.20141944, 0.1590185 , 0.13852083, 0.08702209, 0.13283426, 0.14539815, 0.14247747. Sum of these wages equals 1.
I very appreciate if someone help me out to write code or use Optimization tool to obtain these results.The input matrix Ms is in attached file.
Best Regards,
Tomi

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Torsten
Torsten 2022-9-25
What are you trying to minimize ? What are your constraints ? I don't get it from your decription.
Tomi
Tomi 2022-9-26
移动：Bruno Luong 2022-9-26
I'm sorry for confusion.
Please see the python code used with Scipy - this code produce the results which I want to write in MatLab script and receive the same results. The second equation is used to minimalize omega wages.
I attached python code.
Best,
Tomi

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 采纳的回答

Torsten
Torsten 2022-9-26
编辑：Torsten 2022-9-26
Ran in:

0 个投票

Ran in:
According to the Python code, F is maximized, not minimized. Change in the below code if appropriate.
M = [0.170543 0.327434 0.174194 0 0.421053 0.307167 0.297659
0.155039 0.504425 0.664516 0.530612 0.102493 0.05802 0.053512
0.255814 0.318584 0.212903 0 0.445983 0.337884 0.311037
0.224806 0.548673 0.664516 0.591837 0.141274 0.068259 0.053512
0.383721 0.389381 0.303226 0 0.573407 0.433447 0.41806
0.360465 0.716814 0.883871 0.755102 0.227147 0.078498 0.073579
0.449612 0.566372 0.36129 0 0.775623 0.573379 0.498328
0.484496 0.920354 0.948387 1 0.265928 0.109215 0.107023
0.375969 0.539823 0.303226 0 0.648199 0.481229 0.438127
0.399225 0.769912 0.716129 0.857143 0.224377 0.102389 0.100334
0.356589 0.39823 0.264516 0 0.717452 0.498294 0.444816
0.391473 0.761062 0.703226 0.795918 0.218837 0.098976 0.09699
0.290698 0.327434 0.251613 0 0.770083 0.518771 0.464883
0.395349 0.761062 0.767742 0.795918 0.207756 0.085324 0.09699
0.352713 0.380531 0.277419 0 0.797784 0.501706 0.501672
0.426357 0.778761 0.870968 0.877551 0.265928 0.112628 0.100334
0.403101 0.336283 0.309677 0 0.761773 0.467577 0.491639
0.468992 0.743363 0.877419 0.897959 0.224377 0.119454 0.090301
0.387597 0.345133 0.341935 0 0.775623 0.518771 0.551839
0.496124 0.787611 0.877419 0.857143 0.263158 0.122867 0.113712
0.333333 0.380531 0.341935 0 0.759003 0.566553 0.585284
0.624031 0.80531 0.780645 0.795918 0.293629 0.12628 0.130435
0.534884 0.40708 0.419355 0 0.894737 0.641638 0.628763
0.786822 0.938053 1 0.632653 0.379501 0.197952 0.120401
0.453488 0.380531 0.419355 0 0.842105 0.607509 0.628763
0.554264 0.876106 0.741935 0.877551 0.254848 0.334471 0.130435
0.639535 0.646018 0.593548 0 1 0.8157 0.73913
0.689922 1 0.735484 0.693878 0.351801 0.337884 0.137124
1 0.867257 0.354839 0 0.617729 1 1
0.546512 0.876106 0.703226 0.877551 0.254848 0.334471 0.130435];
w0 = [1/7;1/7;1/7;1/7;1/7;1/7;1/7];
Aeq = ones(1,7);
beq = 1.0;
lb = zeros(7,1);
ub = ones(7,1);
options = optimset('TolFun',1e-10,'TolX',1e-10);
format long
[w,fval] = fmincon(@(w)fun(w,M),w0,[],[],Aeq,beq,lb,ub,[],options)
Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance.
w = 7×1
0.200081504852845 0.157959395465906 0.137599668689948 0.086444832698773 0.131950619523270 0.144443169868022 0.141520808901237
fval =
-3.039398091210332
function value = fun(w,M)
cM = zeros(7,1);
Mw = M*w;
Mwm = mean(Mw);
Mim = mean(M,1);
for i = 1:7
Mi = M(:,i);
cM(i) = sum((Mi-Mim(i)).*(Mw-Mwm))/sqrt(sum((Mi-Mim(i)).^2)*sum((Mw-Mwm).^2));
end
value = -sum(cM);
end

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Torsten
Torsten 2022-9-28
编辑：Torsten 2022-9-28
@Tomi comment moved here:
Dear Torsten,
I'm trying to understand code - need some help.
I very appreciate if you could tell me how the cM(i) equation was created?
Best,
Tomi

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更多回答（2 个）

Tomi
Tomi 2022-9-28

0 个投票

Thank you for your time and help.
I very aprpeciate that.
Best,
Tomi
Tomi
Tomi 2022-9-28

0 个投票

Dear Torsten,
I'm trying to understand code - need some help.
I very appreciate if you could tell me how the cM(i) equation was created?
Best,
Tomi

5 个评论
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Torsten
Torsten 2022-9-28
Don't use answers when you want to make a comment.
See my answer above.
Tomi
Tomi 2022-9-29
Thank you for help and time.
Best Regards,
Tomi
Tomi
Tomi 2022-9-29
Is there any chance to rewrite code without "function" use?
Tomi
Torsten
Torsten 2022-9-29
编辑：Torsten 2022-9-29
Ran in:
Ran in:
M = [0.170543 0.327434 0.174194 0 0.421053 0.307167 0.297659
0.155039 0.504425 0.664516 0.530612 0.102493 0.05802 0.053512
0.255814 0.318584 0.212903 0 0.445983 0.337884 0.311037
0.224806 0.548673 0.664516 0.591837 0.141274 0.068259 0.053512
0.383721 0.389381 0.303226 0 0.573407 0.433447 0.41806
0.360465 0.716814 0.883871 0.755102 0.227147 0.078498 0.073579
0.449612 0.566372 0.36129 0 0.775623 0.573379 0.498328
0.484496 0.920354 0.948387 1 0.265928 0.109215 0.107023
0.375969 0.539823 0.303226 0 0.648199 0.481229 0.438127
0.399225 0.769912 0.716129 0.857143 0.224377 0.102389 0.100334
0.356589 0.39823 0.264516 0 0.717452 0.498294 0.444816
0.391473 0.761062 0.703226 0.795918 0.218837 0.098976 0.09699
0.290698 0.327434 0.251613 0 0.770083 0.518771 0.464883
0.395349 0.761062 0.767742 0.795918 0.207756 0.085324 0.09699
0.352713 0.380531 0.277419 0 0.797784 0.501706 0.501672
0.426357 0.778761 0.870968 0.877551 0.265928 0.112628 0.100334
0.403101 0.336283 0.309677 0 0.761773 0.467577 0.491639
0.468992 0.743363 0.877419 0.897959 0.224377 0.119454 0.090301
0.387597 0.345133 0.341935 0 0.775623 0.518771 0.551839
0.496124 0.787611 0.877419 0.857143 0.263158 0.122867 0.113712
0.333333 0.380531 0.341935 0 0.759003 0.566553 0.585284
0.624031 0.80531 0.780645 0.795918 0.293629 0.12628 0.130435
0.534884 0.40708 0.419355 0 0.894737 0.641638 0.628763
0.786822 0.938053 1 0.632653 0.379501 0.197952 0.120401
0.453488 0.380531 0.419355 0 0.842105 0.607509 0.628763
0.554264 0.876106 0.741935 0.877551 0.254848 0.334471 0.130435
0.639535 0.646018 0.593548 0 1 0.8157 0.73913
0.689922 1 0.735484 0.693878 0.351801 0.337884 0.137124
1 0.867257 0.354839 0 0.617729 1 1
0.546512 0.876106 0.703226 0.877551 0.254848 0.334471 0.130435];
w0 = [1/7;1/7;1/7;1/7;1/7;1/7;1/7];
Aeq = ones(1,7);
beq = 1.0;
lb = zeros(7,1);
ub = ones(7,1);
options = optimset('TolFun',1e-10,'TolX',1e-10);
Mim = mean(M,1);
fun = @(w) -sum(arrayfun(@(i)sum((M(:,i)-Mim(i)).*(M*w-mean(M*w)))/sqrt(sum((M(:,i)-Mim(i)).^2)*sum((M*w-mean(M*w)).^2)),1:7));
fun = function_handle with value:
@(w)-sum(arrayfun(@(i)sum((M(:,i)-Mim(i)).*(M*w-mean(M*w)))/sqrt(sum((M(:,i)-Mim(i)).^2)*sum((M*w-mean(M*w)).^2)),1:7))
format long
[w,fval] = fmincon(fun,w0,[],[],Aeq,beq,lb,ub,[],options)
Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current step is less than the value of the step size tolerance and constraints are satisfied to within the value of the constraint tolerance.
w = 7×1
0.200081504852845 0.157959395465906 0.137599668689948 0.086444832698773 0.131950619523270 0.144443169868022 0.141520808901237
fval =
-3.039398091210332
Tomi
Tomi 2022-9-30
Thank you very much for your help.
Best,
Tomi

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