How to write the nonlinear constraints in a correct way?

I have a complex problem to solve and I'm using the fmincon solver. Firstly I wrote the equality and inequality constraints like it was done in the user guide for Optimisation Toolbox in the following form:

variables = {'I1','I2','HE1','HE2','LE1','LE2','C','BF1',...
'BF2','HPS','MPS','LPS','P1','P2','PP','EP'};
N = length(variables);
% create variables for indexing
for v = 1:N
eval([variables{v},' = ', num2str(v),';']);
end 

Aeq = zeros(4,16); beq = zeros(4,1);
Aeq(1,[LE2,HE2,I2]) = [1,1,-1];
Aeq(2,[LE1,LE2,BF2,LPS]) = [1,1,1,-1];
Aeq(3,[I1,I2,BF1,HPS]) = [1,1,1,-1];
Aeq(4,[C,MPS,LPS,HPS]) = [1,1,1,-1];

etc.

My question is how to assign these variables in separate script file to be able to write the nonlinear constraints in the form like this:

LE1^2+BF1^2=C*MPS : For example

Thank you.

Answer 1

[Alan Weiss]

I am afraid that you didn't quite understand the example. The point is that an x variable has many components, and in this example the components were named.

To write a nonlinear constraint function, use the syntax

 function [c,ceq] = mycfun(x)
 % Name the variables if you like
  variables = {'I1','I2','HE1','HE2','LE1','LE2','C','BF1',...
  'BF2','HPS','MPS','LPS','P1','P2','PP','EP'};
  N = length(variables);
  % create variables for indexing
  for v = 1:N
  eval([variables{v},' = ', num2str(v),';']);
  end
 % Then start the computation
 c = [];
 ceq = x(LE1)^2+x(BF1)^2 - x(C)*x(MPS);

I hope this makes sense to you. For details for nonlinear constraints, see the documentation.

Alan Weiss

MATLAB mathematical toolbox documentation

[Anton Nester]

Thank you for explanation.