How can I solve for six variable using six equations using the Optimization toolbox such that the variables are between 1 and 0?

ConstStr

N7 = 3.135E+00*N1*N2,

N8 = 4.100E-01*N2*N6,

N9 = 1.381E+01*N1*N4,

N10 = 7.610E+01*N2^2*N3,

N11 = 1.720E+05*N2*N3^2*N5^3,

N12 = 4.034E+04*N3*N5^2,

N13 = 2.615E+04*N2*N3^2*N5^2,

N14 = 3.826E+44*N1*N3*N5^2,

N15 = 1.458E+03*N2*N3*N5,

N16 = 2.435E+04*N1*N3^2*N5,

N17 = 1.186E+08*N3^2*N5^3,

N18 = 7.511E+02*N3*N5,

N19 = 6.874E+02*N3*N5;

Function

N1+N2+N3+N4+N5+N6+N7+N8+N9+N10+N11+N12+N13+N14+N15+N16+N17+N18+N19 = 1;

0.1962*(N2+N7+N8+2*N10+N11+N13+N15)-0.6575*(N1+N7+N9+N14+N16) = 0;

0.0557*(N3+N10+2*N11+N12+2*N13+N14+N15+2*N16+2*N17+N18+N19)-0.4698*(N4+N9) = 0;

0.0099*(N5+3*N11+2*N12+2*N13+2*N14+N15+N16+3*N17+N18+N19)-0.3525*(N6+N8) = 0;

0.0557*(N1+N7+N9+N14+N16)-0.1962*(N4+N9) = 0;

0.0099*(N2+N7+N8+2*N10+N11+N13+N15)-0.6575*(N6+N8) = 0;

[TAHMEED TASNIM]

I wish to find the values of N1, N2, N3, N4, N5 and N6 within 0 and 1

[Alex Sha]

Looks like the code of 1stOpt, easy to get the results below:

n1: 0.0102966514928505
n2: 0.239882301416368
n3: 0.0756391320164553
n4: 0.067590437058481
n5: 9.05432951887928E-22
n6: 0.0124929422699874

Answer 1

[Abhisek Pradhan]

The following link has a detailed documentation and solved example of non-linear system of equations using Optimization Toolbox.

https://in.mathworks.com/help/optim/getting-started-with-optimization-toolbox.html