Constraint on some of the design variables

Hi all,

If I have an objective function as

obj(x,y,z) with lower bounds [x_l,y_l,z_l] and upper bounds [x_u,y_u,z_u]

and a non-linear constraint applied only to y & z: nlincon(y,z) , which is a scalar valued function.

How do I implement this optimization problem in matlab?

Thanks

Answer 1

[Walter Roberson]

Sounds like a standard fmincon(). Your input variables would be the vector [x, y, z] and inside your nonlinear constraint function you would just ignore the portion of the input that corresponds to x.

[Aneesh Vasudev]

I would like to use a nonlinear inequality constraint. The documentation says that the output of the nonlinear constraint, c(x)<=0, is a vector as well. Hence, in this case, the outputs corresponding to x and maybe y are 0, therefore, effectively applying the constraint only on z? 'x' because the nonlinear constraint is not a function of x, and 'y' because the nonlinear constraint is scalar valued (choice of applying the constraint either on y or z).

[Walter Roberson]

Although c and ceq outputs of the nonlinear constraints should be vectors, they can be whatever length of vector you need for your situation (including possibly scalar or empty.)

It is entirely valid to accept a vector of length 21 on input but to emit a vector of (say) length 2, like

function [c, ceq] = nonlcon(xyz)
   x = xyz(1:5);  %x is the first five values
   y = xyz(6:8);  %y is the next three values
   z = xyz(9:11); %z is the next three values
   c(1) = y(2) - z(1);
   c(2) = y(1)*y(3) + z(2).^2;
   ceq = [];

[Aneesh Vasudev]

Ok, I understand. I'm just curious though, how does fmincon know to which design variables the constraint is being applied? By design variables, I mean, xyz(1),xyz(2),...,xyz(11).

[Walter Roberson]

Nonlinear constraints often involve the relationship between multiple variables. If you had a constraint such as

x(1)^2 + x(2)^2 <= 25

then is that a constraint on x(1) or is it a constraint on x(2) ??

Suppose that you had a series of constraints,

x(1)^2 - 2*x(1) <= 5
x(2)^2 - 2*x(2) <= 5

and so on for each variable, and you also had a constraint

x(1)*x(2) >= 1/2

If the requirement was to emit one c entry for each x entry so that fmincon could somehow know which variable the constraint was being applied to, then how would you emit more constraints than there were variables?

[Aneesh Vasudev]

Sure. It seems like I have to revisit some math.