Search for a numerical solution of the system of equations for a parameter given on the interval

HI, I have 6 non-linear equations and 6 unknowns. Search for solution on restrictions demanded for me did`t give a result. I want specified parameter (q=0.3) in equations like interval 0.25<q<0.45 and get real numerical result for minimum q. What MATLAB tool should I use?

[Walter Roberson]

That is tricky unless the system is such that if q0 is the minimum q with a solution, then every q0 < q < 0.45 also has a solution ? But if the solution ranges are discontinuous, the situation gets considerably harder, unless it is feasible to do some numeric analysis to make the search easier.

[Pavel Aksentsev]

I Can`t answer on "That is tricky unless the system is such that if q0 is the minimum q with a solution, then every q0 < q < 0.45 also has a solution ? " , possibly yes, i don`t know. I can only write more restrictions, to simplify search(Also, I may not require a solution for the minimum q, I will be happy to receive an answer for any 0.25<q<0.45). So the question about implementation is still relevant.

Answer 1

[Walter Roberson]

If you just need any solution in that range, then fzero the set of 6 equations, but expand from 6 variables to 7 variables with q as the 7th variable, and use lb and ub to restrict its range.

[Walter Roberson]

You can also write a system like this as norm() of the set of left hand sides minus right hand sides.

In the case where the values are known to be real, the norm would be the square root of the sum of squares of (left minus right), and for minimization purposes it is enough to compare the sum of squares without taking the square root.