Solving a system of nonlinear equations with unorganized unknowns?

Ideally when using fsolve, my entire solution vector will be unknown. However my unknowns are broken down into 2 vectors x and r such that some values of my x vector are always fixed as they are boundary conditions but the summation of the length of x which are unknown, and r gives me the total number of unknowns. Is there a way I can use fsolve to pick the indices I would like it to solve leaving the boundary conditions the way they are?.

Answer 1

[Matt J]

If you use lsqnonlin instead of fsolve, you can set a vector of upper and lower bounds ub and lb on the solution. Just set ub(i)=lb(i) for those x(i) elements you want constrained to something known, e.g.,

p0=[x0(:);r0(:)]; %Initial guess

N=numel(p0);

[lb,ub]=deal(-inf(N,1), +inf(N,1));

ub(1:3)=10; lb(1:3)=10; %constrain x(1:3) to equal 10


p=lsqnonlin(@yourFunction,p0,lb,ub)

[Devanjith Fonseka]

Thanks for the prompt reply.

Just 2 questions.

This works for a system of nonlinear equations and yourFunction is defined the same way as I would for fsolve right?

Why isn't p0 defined as p0=[x0(:),r0(:)]?

Thanks!

[Matt J]

This works for a system of nonlinear equations and yourFunction is defined the same way as I would for fsolve right?

Yes.

Why isn't p0 defined as p0=[x0(:),r0(:)]?

It doesn't matter. The solver will reshape p0 into a column vector anyway, as described here

https://www.mathworks.com/help/optim/ug/matrix-arguments.html

[Devanjith Fonseka]

Hello,

I implemented it and I get this error:

The Levenberg-Marquardt algorithm does not handle bound constraints and the trust-region-reflective algorithm requires at

least as many equations as variables; aborting.

I expected this to occur considering that even though I constrain my vector to take a specific value for my known variables, I would be left with too many variables.

Is there any work around to this?

[Matt J]

If you have fewer equations than unknowns then it is not clear what you hope for as a result. There will normally be infinite solutions in that situation, and the problem will be ill-posed.