Multi Objective nonlinear functions with unknown multi parameters

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SN MJTHD
SN MJTHD 2019-7-22
回答： Alex Sha 2019-8-28
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,
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Torsten
Torsten 2019-7-23
lsqnonlin is especially designed to solve problems like yours, but you are of course free in the choice of the optimizer.

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回答（1 个）

Alex Sha
Alex Sha 2019-8-28
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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