Adding a constraint in @confun constrained optimization

Hello, I am struggling to add a second constraint in my optimization problem... My obj function is:

function f = objfun(X)
for i=1..18;
   f=sum(exp-(10*X(i)); end

My 1st constraint is a non linear inequality :

function [c,ceq]=confun(X)
ceq = [];
c(1) =(-0.35*X(3)+0.35*X(9)+1.3333*X(10))^2-(0.3333*X(13)+0.3182*X(3)-0.6364*X(6)+0.3182*X(9)-X(17))^2-(0.015/2)^2;

My second constraint is also a non linear inequality which I can't code, here is what I want to verify:

    % I need that all the values from 0 to the X(i) to be generated (the optimum X(i)), the condition 1 is verified.

Would you note that ub and lb and all the other entries for fmincon are known and my problem is only in the @confun

[x,fval]= fmincon(@objfun,x0,A,b,Aeq,beq,lb,ub,@confun,options)

A = [];
b = [];
Aeq = [];
beq = [];
x0 = [0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016,0.0016];
lb = [0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015,0.0015];
ub = [0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015,0.015];
options = optimoptions(@fmincon,'Algorithm','sqp');

[Alan Weiss]

Sorry, I don't understand what you mean by your second constraint. The only description you gave is "I need that all the values from 0 to the X(i) to be generated (the optimum X(i)), the condition 1 is verified." I have no idea what that means.

Alan Weiss

MATLAB mathematical toolbox documentation

[Mondher Souilah]

Hello Alan, in other words: I would like that the values to be generated at the end of the optimization respect the second constraint.

to be more clear, here is an example: i could have for example X(3)=0.013 at the end. this could respectcondition n1 but i want also to verify that : within all the interval (0.000 to 0.013) the condition is respected.

Answer 1

[Bruno Luong]

Mathmematically you could define another constraint function

h(x) := sup { g(y): y in [0,x] }

then optimize your objective function:

argmin obj(x), with the constraint

h(x) <= somevalue

Now the problem becomes "how to compute h(x)?"

But that's is now on your side, and you might able to do it with specific formula of g(x).

You can of course use fmincon or such to compute h(x). But that might be costly. In this case the confun becomes (quick and dirty):

function [c,ceq]=confun(X)

lb = zeros(size(X));
ub = X;
afun = @(X) -0.35*X(3)+0.35*X(9)+1.3333*X(10);
bfun = @(X) 0.3333*X(13)+0.3182*X(3)-0.6364*X(6)+0.3182*X(9)-X(17);
g = @(X) (afun(X).^2-bfun(X).^2);
X = fmincon(@(X) -g(X), X, [], [], [], [], lb, ub); % Maximize g(X)
c = g(X)-(0.015/2)^2;

end

In some problems, it is sometime easier to find a formula for another function that is slightly greater than h(x):

H(x) >= h(x) for all x.

Note: "sup" is loosely speaking "max" for people who are not familiar with the notation.

Answer 2

[Alan Weiss]

It sounds to me as if your problem could be formulated for fseminf.

Alan Weiss

MATLAB mathematical toolbox documentation