I need to find a point (any point will do) located inside a convex set Z. Z is the intersection of N convex set that is defined by Z_i ().

Z_i ={x | ||x-a_i||^2 <= k_i}, i=1,…,N

x (belongs to R^2)

a_i (belongs to R^2) and k_i (belongs to R) are given.

I have formulated the following SDP to solve it. Is there any other way to solve the problem.

cvx_begin sdp

variable x(2,1)

subject to

for i=1:N

[k(i) (x-a(:,i))’;(x-a(:,i)) eye(2) ] >= 0

end

cvx_end