Nonlinear system of equations with constrains

Hi every body,

I have 4 nonlinear equations and 4 unknowns to be solved. but my unknowns are constrained. So I can't use something like fsolve. Which function do I need to use? I also have optimization toolbox. Is 'fgoalattain' my answer?(I've tried it but not familiar how it works:( )

thanx

Answer 1

[Matt J]

If the constraints are simple upper and lower bounds, you can use lsqnonlin(). Otherwise, you could use fmincon().

[Mohammad Monfared]

Thanks for your reply,

I've tried 'lsqnonlin' but all of the results are not satisfactory. While 3 of my equations are acceptably solved, there is one which is not. The problem with 'lsqnonlin' is that it doesn't minimize(solve) each equation separately but minimizes (f1(x)+f2(x)+...).

I feel I need something to control each equation separately.

The objective function for 'fmincon', should return a scalar (like (f1(x)+f2(x)+...) ) not a vector.

[Matt J]

The problem with 'lsqnonlin' is that it doesn't minimize(solve) each equation separately but minimizes (f1(x)+f2(x)+...).

No, that isn't to be viewed as a problem. If the system of equations possesses a simultaneous solution then that solution must globally minimize the sum of squares (f1(x)+f2(x)+...), bringing it to a minimum value of zero. Similar remarks apply to fmincon.

If you're not getting the results you want it is likely because of one or more of the following,

1. You have coded your objective function incorrectly
2. You have given a bad initial guess x0
3. Your system does not have a simultaneous solution. You must relax your requirements and accept a least squares solution in that case.