Help implementing this problem

[optimizer]

Dear Sir.Johan, i have a question on how to implement this problem:

%Objective

yavar=sdpvar(3,1);

f=Lproj*yavar-U;

y=[0;0.0005;0;0.0056464;0;0.011;0;0.0082782;0.0005;-0.0046464];

%Constraint

limit=0.9;

epsilon=limit*[-9.9332e+06;1.8386e+07;-9.9332e+06];

r=A'*yavar+B*y;

Constraints = [A*r <= epsilon*norm(r)];   

%Optimization

assign(yavar,xa0)

options = sdpsettings('verbose',1,'solver','fmincon');

sol = optimize(Constraints,f'*f,options);

Matrices of real numbers:

size(Lproj)=  13 rows    3 columns

size(A)=        3  rows    10 columns

size(B)=        10  rows      10 columns

size(U)=        13  rows      1 columns

I get this error:

sol = 

  struct with fields:

    solvertime: 0

       problem: 14

          info: 'Model creation failed (Only 1- and inf-norms can be used in a nonconvex fashion)'

    yalmiptime: 0.04

How can i avoid using norm(r)?

[Johan Löfberg]

You would have to square you model accordingly, such as

sdpvar t

[A*r <= epsilon*t, t^2 = r'*r]

non-convex of course, since your model is non-convex

[optimizer]

There is a simple way to understand if the problem is convex or not?

[Johan Löfberg]

To prove sufficiency for convexity, you use propagation of convexity through composition rules, which is what YALMIP uses

To disprove convexity, you typically use trivial counterproofs. norm(x) > is generally non-convex, just draw the set  |x| >= 1 for scalar x.