simple optimization question

[optimizer]

This is my MWW, i would like to find parameters x and y leading the expression (A+X)*v1+(B+Y)*v2 to zero.

How to do that with optimize?

% Minimal Work Example

A=[7    -2   3   2   -3;

   2    -1  0   1   0;

   -2   5   11  -5  -6;

   3    2   -2  1   0;

   5    7   8   -9  1;

   2    9   0   1   -5];

v1=[1;-1;2;1;4];

B=[3    1   3;

   -2   5   4;

   0    7   -1;

   2    9   0;

   -2   5   11;

   7    2   3];

v2=[2;1;-1];

x=sdpvar(2,1);

y=sdpvar(2,1);

X=[0        0       x(2)   0   0;

   -x(1)    0       0       0   0;

   0        -x(1)   0       0   0;

   x(2)     0       x(1)   0   0;

   x(1)     -x(2)   0    0   0;

   -x(1)    0       0       0   0];

Y=[y(1)     y(2)       0;

   0        0       -y(1);

   0        y(2)       0;

   y(1)     0       -y(2);

   -y(1)    y(1)    0;

   0        -y(1)  0];

xL=[-10;-10];              

xU=[10;10];              

yL=[-10;-10];            

yU=[10;10];      

ConstrX=[xL<=x<=xU];   

ConstrY=[yL<=y<=yU];

p=(A+X)*v1+(B+Y)*v2;

oldval=A*v1+B*v2;

I think about using:

sol=optimize(ConstrX+ConstrY,p);

Is this correct?

[Johan Löfberg]

No, you are currently minimizing p (which makes no sense since p is a vector), but you say you want to find a solution which simply satisfies p == 0 (which is infeasible)

[optimizer]

So i have to use:

sol=optimize(ConstrX+ConstrY,p'*p);

And after that to find feasible constraints for my problem?

[Johan Löfberg]

You said you wanted  ConstrX + ConstrY + (p==0)

Your model here would minimize the 2-norm of p,  which perhaps could be a sensible replacement for the equality constrained problem when it is infeasible