You should use pctRunOnAll at the client, i.e. before the start of the loop, like this:
gcp(); % Ensure we have a parallel pool that parfor will use
pctRunOnAll warning_off_WarnIfIllConditioned
parfor V_g_i = 1:length(V_g_vec)
%% Other code
[Vi,~] = eigs(mat,1,10^(-19)); % mat is an ill-conditioned matrix
%% Other code
end
(I assume warning_off_WarnIfIllConditioned is a script or function you have to make the necessary warning modifications)
