如何解决sqrt(1/norm)?

Nonconvex
1

num_points=10;Np=20;alpha1和g0都为常数
hk_jiaodu为[N,1]的已知数组
hk(:,j,i)为[N,num_points-1,Np]的存储数组
variables q(3,Np);
expression temp1;
expression temp2;
expression temp3;
expression temp4;
expression temp5;
for j=1:num_points-1
for i=1:Np
temp1=norm(q(:,i)-location(:,j));
temp5=sqrt(temp1);
temp4=inv_pos(temp5);
temp2=pow_pos(temp4,alpha1)/g0;
temp3=sqrt(temp2);
hk(:,j,i)=temp3.*hk_jiaodu;
end
end
报错信息sqrt( {convex} )，请问如何解决

2

sqrt(1/norm) by itself is not convex, So I think your only hope is if it is used in such a way as to allow a broader refromulation. I.e., you must first prove that the overall optimization problem is convex.

3

尊敬的Mark先生，非常感谢您的回复，我知道sqrt(1/norm)本身非凸，所以我尝试将其分开，可是sqrt(norm)也会报错，即原代码的temp5=sqrt(temp1)部分会报错sqrt({convex});请问如果仅考虑使这一部分可以被cvx许可，我应该怎么修改

4

Please read the link again. You will only be able to formulate this in CVX if the optimization problem is convex.

Do you actually need the sqrt? For example, if the constraint is sqrt(1/norm(x)) >= 2, you can reformulate it as 1 >= 4*norm(x). If you don’t have a situation such as this which allows a reformulation, you are out of luck with CVX.

5

好的，我理解了，我会尝试一下问题的转化，非常感谢您的帮助