Cannot norm( {convex}, 1 )

Nonconvex
1

This is my formula:
图片

But I have to divide v into vx in the horizontal direction and vy in the vertical direction. The error always in convex. Please help me solve this problem!

Code:
H=0:100:200;
cvx_begin

      variable vx_opt3(1,length(H)) 
      variable vy_opt3(1,length(H))

      v=pow_pos(vx_opt3(1,zz),2)+pow_pos(vy_opt3(1,zz),2);  

      for l=1:L % 2
            for k=1:K  %12 组
              for wn=1:WN %2
                 for n=1:N  % 2  
                    pkn=sum(p_opt3((k-1)*N+1:(k-1)*N+n,zz)); 
                    for nv=n+1:N  
                       pknv=sum(p_opt3((k-1)*N+(n+1):(k-1)*N+nv,zz)); 
                    end
                 end 
                tempRate3v((l-1)*K*WN+(k-1)*WN+wn)=log(alpha*(H(zz)^2+re33((l-1)*K*WN+(k-1)*WN+wn))+pknv)/log(2);
                f3v((l-1)*K*WN+(k-1)*WN+wn)=sum(tempRate3v(1:(l-1)*K*WN+(k-1)*WN+wn)); 
              end
            end  
          end

          v=pow_pos(vx_opt3(1,zz),2)+pow_pos(vy_opt3(1,zz),2);  
          g3=2*(c1*pow_pos(norm(v),3)+c2*inv_pos(v))+f3v(48);

Error:

图片
图片857×373 18.5 KB

2

1/norm(v) is neither convex nor concave.

norm(v)^3 is convex. I’m not sure whether c1*norm(v)^3 + c2/norm(v) is convex for any positive values of c1 and c2, but it is not convex for all positive values of c1 and c2.

3

Thank you very much，Mark！