### From Wikimization

E_full.mat

E_small.mat

%%% Theorem of the Alternative.
clear all
clc
load E_small
%load E_full
[m n] = size(E);
found=[];
cvx_quiet('true')
cvx_precision('low')
for i=1:n
inconclusive = true;
cvx_begin
variable a(n+1,1);
a(1:n) >= 0;
-E(:,i) == [E t]*a;
cvx_end
if strcmp(cvx_status,'Solved') || strcmp(cvx_status,'Solved/Inaccurate')
problem_solved = 1;
inconclusive = false;
else
cvx_begin
variable z(m,1);
t'*z == 0;
E(:,i)'*z == 1;
E'*z >= 0;
cvx_end
if strcmp(cvx_status,'Solved') || strcmp(cvx_status,'Solved/Inaccurate')
problem_solved = 2;
inconclusive = false;
end
end
fprintf('%6d/%6d',i,n);
if inconclusive, fprintf(' numeric failure\n'), else fprintf(' problem %d solved\n',problem_solved), end
end