Help:cvx codes about convex

1

cvx_begin quiet
variable X1(2,1);
expression ri(n,1);
variable y;
expression yi(n,1);
expression h(n,1);
minimize sum(h);
subject to
y>=sum_square_abs(X1);
for j=1:n
yi(j)=y-2Anchors(j,1:2)X1+Anchors(j,1:2)(Anchors(j,1:2))’;
ri(j)=norm(Anchors(j,1:2)-X1’);
h(j)=(bi(j)^2)yi(j)-2bi(j)ri(j);
pow_pos(ri(j),2)<=yi(j);
% norm([2ri(j);yi(j)-1],2) <=yi(j)+1;
end
% sqrt(4(pow_pos(ri,2))+pow_pos((yi-1),2))<=yi+1;
% sqrt(4*(ri.^2)+(yi-1).^2)<=yi+1;

        norm([2*X1;y-1],2)<=y+1;
        norm([2*ri;yi-1],2)<=yi+1;
    cvx_end

错误使用 cvx/norm (line 52)
Disciplined convex programming error:
Cannot perform the operation norm( {mixed convex/affine}, 2 )

出错 RSS_socp (line 77)
norm([2*ri;yi-1],2)<=yi+1;

3

Hello, do you have a solution?

4

norms is a useful CVX function, but it is irrelevant to the error at hand, which is that the argument of norm must be affine, which ri is not. The "illegal’ expression is a norm of a norm, which violates CVX’s rules. norms could however allow ri(j)=norm(Anchors(j,1:2)-X1’); to be pulled out of the for loop.

Fortunately, this can be reformulated to not have norm of norm. Just introduce ri_no_norm(j) as ri_no_norm(j)=Anchors(j,1:2)-X1'; And then use norm([2*ri_no_norm;yi-1],2)<=yi+1; I added ri_no_norm rather than changing ri, because ri is also used elsewhere in your program…

5 
        for j=1:n
            yi(j)=y-2*Anchors(j,1:2)*X1+Anchors(j,1:2)*(Anchors(j,1:2))';

% ri(j)=norm(Anchors(j,1:2)-X1’);
ri_no_norm(j)=Anchors(j,1:2)-X1’;
h(j)=(bi(j)^2)yi(j)-2bi(j)ri(j);
% pow_pos(ri(j),2)<=yi(j);
% norm([2ri(j);yi(j)-1],2) <=yi(j)+1;
end
% sqrt(4*(ri.^2)+(yi-1).^2)<=yi+1;
norm([2X1;y-1],2)<=y+1;
norm([2ri_no_norm;yi-1],2)<=yi+1;
% sqrt(4*(pow_pos(ri,2))+pow_pos((yi-1),2))<=yi+1;
cvx_end

wrong usage cvx/subsasgn (line 39)
The assignment cannot be performed because the index on the left is not compatible with the size on the right.

Error RSS_socp (line 69)
ri_no_norm(j)=Anchors(j,1:2)-X1’;

Hello, thank you for your reply. I corrected this kind of error, I don’t know if it was corrected.

6

We donn’t know what function you want to express. Can you explain what you want to do, or show us your mathematical formulas? I guess what Dr.Stone were trying to say is ri_no_norm(j) >= norm(Anchors(j,1:2)-X1'); rather than ri_no_norm(j)=Anchors(j,1:2)-X1';.

7

I think this will work:

expression ri_no_norm(2*n,1)
for j=1:n
ri_no_norm(2*j-1:2*j) = Anchors(j,1:2)'-X1;
end

You should be able to vectgorize this (reformulate it to not use for loop) if executing this for loop takes too long for you.

And the point of the reformulation to not use norm of norm is that the expression using norm with ri_no_norm` is mathematically equivalent to the norm of norm formulation, but it is accepted by CVX.