Multi Objective nonlinear functions with unknown multi parameters

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SN MJTHD
SN MJTHD le 22 Juil 2019
Réponse apportée : Alex Sha le 28 Août 2019
Dear Matlabers,
Lets say my system of equations are as below:
((1-x(1))*(10+x(5)))^2/(((x(1)^2)*x(3)^2)+((1-x(1))^2*x(2)^2)) = 0.154;
((1-x(1))*(10-x(5)))^2/(((x(1)^2)*x(3)^2)+((1-x(1))^2*x(2)^2)) = 0.254;
(x(1)*(10+x(4)))^2/(((x(1)^2)*x(3)^2)+((1-x(1))^2*x(2)^2)) = 0.545;
(x(1)*(10-x(4)))^2/(((x(1)^2)*x(3)^2)+((1-x(1))^2*x(2)^2)) = 0.034;
(10+(x(1)*x(4))+(1-x(1))*x(5))^2/(((x(1)^2)*x(3)^2)+((1-x(1))^2*x(2)^2)) = 0.994;
(10-(x(1)*x(4))-(1-x(1))*x(5))^2/(((x(1)^2)*x(3)^2)+((1-x(1))^2*x(2)^2)) = 0.063;
and I want to find x(1) ... x(5) values so that the equalities hold.
I already tried so many optimization methods but the problem is, after finding the values when I replace them with x values the error values I came across are very large.
Any help is appreciated..
Best,
  10 commentaires
Torsten
Torsten le 23 Juil 2019
lsqnonlin is especially designed to solve problems like yours, but you are of course free in the choice of the optimizer.
SN MJTHD
SN MJTHD le 23 Juil 2019
Thank you for your time and your effort.
Best

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Réponses (1)

Alex Sha
Alex Sha le 28 Août 2019
There are multi-solutions:
1:
x1: 0.387245311047365
x2: -0.00972723068513297
x3: -40.2902696169456
x4: 18.9579782048437
x5: -2.65707955299356
2:
x1: 0.387245311627332
x2: 7.2906925850934
x3: 38.6033440479639
x4: 18.9579781524691
x5: -2.65707955385685
3:
x1: 0.387245311366753
x2: -24.1738267443381
x3: 12.6548907569997
x4: 18.9579781707223
x5: -2.65707955330091

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