YALMIP constraint: Writing constraints for the first and last position

If I have:

y = [y_(1), ..., y_(N)]^T and z = [z_(1), ..., z_(N)]^T

I want to minimize a function V(y_(i), z_(i)) in which my constraints are

(y_(1), z_(1)) = (-2, 1) and

(y_(N), z_(N)) = (2, 1)

Consider N = 40.

I am required to write a constraint, so I would I have

y = sdpvar(1,N) and z = sdpvar(1,N)

now I just have to set (y1,z1) = (-2, 1) and (yN, zN) = (2,1). How can I write this in MATLAB?

Answer 1

[John D'Errico]

Don't. At least, don't write ANY constraints at all.

Just minimize the function for y(2:N-1) and z(2:n-1). Inside your objective function, create y and z as:

y = [-2, ..., 2]^T and z = [1, ..., 1]^T

Consider N as anything you want.

Be careful. If someone tells you to just set lower and upper bounds equal to each other, that often just results in numerical problems, unless the code explicitly states that this is a valid way to fix a variable at some level. In that case, the code will essentially remove those variables from the optimization for you.

[yuanb]

So I can do

y=sdpvar(-2,2) and z = sdpvar(1,1)

and

C = [y(2:N-1), z(2:N-1)]

Is this correct?

[yuanb]

I am required to write a constraint, so I thought I would I have

y = sdpvar(1,N) and z = sdpvar(1,N)

now I just have to set (y1,z1) = (-2, 1) and (yN, zN) = (2,1). How can I write this in MATLAB?

[John D'Errico]

No. You are not required to write a constraint. You are required to solve a problem with those variables held fixed. READ WHAT I WROTE IN MY ANSWER. Read it again.

If you insist on writing a constraint, then learn how to use linear equality constraints. Set up 4 equality constraints, one for each variable that you wish to fix.

[yuanb]

Thank you for your help. I said I am "required" meaning that the assignment asks me to write one.

Answer 2

[Johan Löfberg]

Model = [y(1) == -2, y(end) == 2, ...]

or simply assign those elements,

y(1) = -2;y(end)=2;...

YALMIP specific question should preferably be posted on the YALMIP google groups forum instead.