how to minimize function for equal value

Question

I'm trying to minimize afunction in matlab like this:

function [c, ceq] = const_slot( x )
c = [];
% Nonlinear equality constraints
ceq = [sum(x)-1];
end



[x,fval] = fmincon(@func_slot, x0,[],[],[],[],lb,ub,@const_slot,options)

But, I need to value fval that was within the specified value, or the positive. How can I do that?

Answer 1

As I understand your question you want to put constraints on your function @func_slot (which I assume is non-linear).

In the Matlab help for fmincon we find:

x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

Non-linear constraints can be set using the nonlcon parameter (in the question you use @const_slot). These constraints should be defined as:

function [c,ceq] = mycon(x)
c = ...     % # Compute nonlinear inequalities at x.
ceq = ...   % # Compute nonlinear equalities at x.

So for example, when you want your function @func_slot to be greater than zero, you can define the inequality constraint c in @const_slot as the negative of your function.

Edit

If I understand you correctly, you need the function value to be greater than zero but less than a specified limit. In that case you could try this.

function [c, ceq] = const_slot( x )

% # Nonlinear inequality constraints
upperLimit = 10;
c = [-func_slot(x);
     -upperLimit + func_slot(x)];

% # Nonlinear equality constraints
ceq = [sum(x)-1];

end