Position of Minimize

1

Hi everybody.
I’ve got a problem with the position of minimize in my cvx cycle.

Precisely, I have an interval matrix as jacobian.I’m using matlab and I built a cell J{k}, with k from 1 to 16 and every J is a 2x2 matrix.

alpha1 =.1
alpha0 =0.004;
beta1=.2;
beta0=0.004;
gamma1=.02;
gamma0=0.004;
delta1=.02;
delta0=0.004;


J{01}=[alpha0 -beta0 ; gamma0 delta0];
J{02}=[alpha1 -beta0 ; gamma0 delta0];
J{03}=[alpha0 -beta1 ; gamma0 delta0];
J{04}=[alpha1 -beta1 ; gamma0 delta0];
J{05}=[alpha0 -beta0 ; gamma1 delta0];
J{06}=[alpha1 -beta0 ; gamma1 delta0];
J{07}=[alpha0 -beta1 ; gamma1 delta0];
J{08}=[alpha1 -beta1 ; gamma1 delta0];
J{09}=[alpha0 -beta0 ; gamma0 delta1];
J{10}=[alpha1 -beta0 ; gamma0 delta1];
J{11}=[alpha0 -beta1 ; gamma0 delta1];
J{12}=[alpha1 -beta1 ; gamma0 delta1];
J{13}=[alpha0 -beta0 ; gamma1 delta1];
J{14}=[alpha1 -beta0 ; gamma1 delta1];
J{15}=[alpha0 -beta1 ; gamma1 delta1];
J{16}=[alpha1 -beta1 ; gamma1 delta1];

I have to study the vector v :

v = min (evaluated in v) of the max(evaluated in J) of the norm (a + J*v,

with a = 2x1 vector that changes its value at the end of every cycles of cvx.

I try this and it works.

cv begin
    cvx_precision default
    variables v(2,1) real;
    expression G(length(J));
      
    for kk=1:16
        G(kk)=norm(J{kk}*v+a);
    end
    minimize max(G);    

cvx_end

but if I try this:

cvx_begin
     cvx_precision default
     variables v(2,1) real;
     expression G(length(J));

    minimize max(G);     
    for kk=1:16
        G(kk)=norm(J{kk}*v+a);
    end

cvx_end

the cvx_optval (in all the cycles) are equal to zero, even though all G(kk) aren’t equal to zero.

Why the cvx gives me that value of optval?
Thank you a lot for your help

Luca

2

G is assigned as an expression.Therefore, it needs to be assigned before use in the objective function. This is done in the 1st program, and not done in the 2nd program. If G were a constraint rather than an expression, it could appear before of after an objective function which is well-defined at the tine the objective function is encountered.

3

Thank you very much. Can I ask you how the problem is seen by cvx if the expression is assigned after the minimize? Has it a mathematical concept or is it a simple big confusion?

Thank you again for your time :slight_smile:

4

An expression assigned after the minimize can still affect any constraints which follow the assignment and involve the assigned expression.

5

Perfect, thanks again!:slight_smile: