Solving a system of nonlinear equations with unorganized unknowns?

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Devanjith Fonseka 2019-10-4

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编辑： Matt J 2019-10-6

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?.

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Answer 1

Matt J 2019-10-4

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https://ww2.mathworks.cn/matlabcentral/answers/483652-solving-a-system-of-nonlinear-equations-with-unorganized-unknowns#answer_394874

编辑：Matt J 2019-10-4

在 MATLAB Online 中打开

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)

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Devanjith Fonseka 2019-10-4

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 2019-10-5

编辑：Matt J 2019-10-6

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.

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