Solving a system of non linear equations with several solver (choose) adjusting the number of equations

Hi all,

I have a certain equation (analytic expression) defined by parameters and some measurements (right side of my equation) and I want to write down a system of equations specifying the number of equations (that can be adjusted). I want to solve the system choosing different solvers possibly, like lsqnonlin or other funcitons within the optimization toolbox. How can I achieve this?

Thanks in advance for your answer.

Answer 1

[Francisco J. Triveno Vargas]

Somethin like that:

clear

close all

% solving 10 nonlinear equations

% x = [p1 p2 p3 x1 x2 x3 l1 l2 l3 l4]

n = 10; % number of variables

RQ = 10; % available water

fun = @(x)lagrange(x,RQ);

x0 = ones(n,1); % initial values

x = fsolve(fun,x0);

% compute objective function

f = (12 - x(1))*x(1) + (20 - 1.5*x(2))*x(2) + (28 - 2.5*x(3))*x(3) ...

-(3*x(1)^1.3 + 5*x(2)^1.2 + 6*x(3)^1.15);

P = x(1:3);

X = x(4:6);

Lambda = x(7:10);

function [F] = lagrange(x,RQ)

F(1) = 12 - 2*x(1) - 1.3*3*x(1)^0.3 - x(7);

F(2) = 20 - 3*x(2) - 1.2*5*x(2)^0.2 - x(8);

F(3) = 28 - 5*x(3) - 1.15*6*x(3)^0.15 - x(9);

F(4) = x(7)*0.9*0.4*x(4)^-0.1 - x(10);

F(5) = x(8)*0.8*0.5*x(5)^-0.2 - x(10);

F(6) = x(9)*0.7*0.6*x(6)^-0.3 - x(10);

F(7) = x(1) - 0.4*x(4)^0.9;

F(8) = x(2) - 0.5*x(5)^0.8;

F(9) = x(3) - 0.6*x(6)^0.7;

F(10) = x(4) + x(5) + x(6) - RQ;

end