Solving constrained non linear system using fmincon doesn't work

Hi all,

I have a non linear differential equation:

dm(1) = f1(m(1),m(2),m(3))
dm(2) = f2(m(1),m(2),m(3))
dm(3) = f3(m(1),m(2),m(3))

whose solutions must lie on the unit sphere. I'm trying to compute the fixed points of the system so I have to solve the system:

f1(m(1),m(2),m(3)) = 0
f2(m(1),m(2),m(3)) = 0
f3(m(1),m(2),m(3)) = 0

I first tried to use fsolve but this gave irrelevant solutions, not even lying on the unit sphere. I then tried to use fmincon by squaring my dm-vector so that it becomes positive. Here is what my code looks like:

Differential equation:

function dm = llgfix(t,m,param)
dm = zeros(3,1);

dm(1) = f1(m(1),m(2),m(3));
dm(2) = f2(m(1),m(2),m(3));
dm(3) = f3(m(1),m(2),m(3));

dm = dm.^2;
end

Constraints:

function [c, ceq] = unitsphere(x)
c = [];
ceq = x(1)^2 + x(2)^2 + x(3)^2 - 1;

Minimisation:

m0 = rand(1,3);
options = optimset('Display','iter','Algorithm','active-set');
fix = fmincon(@llgfix,m0./norm(m0),[],[],[],[],[],[],@unitsphere,options)

However, when running the code, I always get the same error:

Error using fmincon (line 674)
User supplied objective function must return a scalar value.

and I can't figure out why, does anybody have an idea?

Thanks in advance!

Answer 1

[Alan Weiss]

This question was answered (satisfactorily, I believe) on comp.soft-sys.matlab.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Sven]

Hi Pi Pi,

Two things. Firstly, your specific error:

User supplied objective function must return a scalar value.

comes because the "objective" function you are providing to fmincon (ie, the function llgfix) is returning a 1-by-3 matrix in the output variable dm. Instead, try:

function dm_sum = llgfix(t,m,param)
dm = zeros(3,1);
dm(1) = f1(m(1),m(2),m(3));
dm(2) = f2(m(1),m(2),m(3));
dm(3) = f3(m(1),m(2),m(3));
dm_sum = sum(dm.^2);
end

Next, when you call fmincon, you use the syntax:

fix = fmincon(@llgfix,...)

fmincon will, by default (ie, with just the @ symbol), only provide one input variable - that's the variable you are trying to modify.

However, your actual llgfix function takes three input variables. I think that this isn't what you intend. Note that you can use syntax like:

fix = fmincon(@(m)llgfix(otherVar,m,otherVar2),...)

To get fmincon to basically call a function with a different set of inputs. Or, you can modify llgfix to only take one input.

Did this get you on the right track?

Thanks, Sven.

Answer 3

[Pl Pl]

Thanks to Sven and my apologies to Alan for not having indicated before that the problem was solved, I completely forgot this discussion.