Box volume maximization
cvxq = cvx_quiet(true);
alpha = 0.5; beta = 2; gamma = 0.5; delta = 2;
N = 10;
Afloor = logspace(1,3,N);
Awall = [100 1000 10000];
opt_volumes = zeros(length(Awall),N);
disp('Computing optimal box volume for:')
for k = 1:length(Awall)
for n = 1:N
cvx_begin gp
variables h w d
maximize( h*w*d )
subject to
2*(h*w + h*d) <= Awall(k);
w*d <= Afloor(n);
h/w >= alpha;
h/w <= beta;
d/w >= gamma;
d/w <= delta;
cvx_end
fprintf(1,' Awall = %5d Afloor = %7.2f max_volume = %3.2f\n', ...
Awall(k),Afloor(n),cvx_optval);
opt_volumes(k,n) = cvx_optval;
end
end
cvx_quiet(cvxq);
figure, clf
loglog(Afloor,opt_volumes(1,:), Afloor,opt_volumes(2,:), Afloor,opt_volumes(3,:));
xlabel('Afloor'); ylabel('V');
Computing optimal box volume for:
Awall = 100 Afloor = 10.00 max_volume = 77.46
Awall = 100 Afloor = 16.68 max_volume = 102.04
Awall = 100 Afloor = 27.83 max_volume = 131.79
Awall = 100 Afloor = 46.42 max_volume = 170.21
Awall = 100 Afloor = 77.43 max_volume = 192.34
Awall = 100 Afloor = 129.15 max_volume = 192.34
Awall = 100 Afloor = 215.44 max_volume = 192.34
Awall = 100 Afloor = 359.38 max_volume = 192.34
Awall = 100 Afloor = 599.48 max_volume = 192.34
Awall = 100 Afloor = 1000.00 max_volume = 192.34
Awall = 1000 Afloor = 10.00 max_volume = 89.44
Awall = 1000 Afloor = 16.68 max_volume = 192.70
Awall = 1000 Afloor = 27.83 max_volume = 415.16
Awall = 1000 Afloor = 46.42 max_volume = 894.43
Awall = 1000 Afloor = 77.43 max_volume = 1926.98
Awall = 1000 Afloor = 129.15 max_volume = 2839.27
Awall = 1000 Afloor = 215.44 max_volume = 3667.06
Awall = 1000 Afloor = 359.38 max_volume = 4736.19
Awall = 1000 Afloor = 599.48 max_volume = 5998.44
Awall = 1000 Afloor = 1000.00 max_volume = 6082.35
Awall = 10000 Afloor = 10.00 max_volume = 89.44
Awall = 10000 Afloor = 16.68 max_volume = 192.70
Awall = 10000 Afloor = 27.83 max_volume = 415.16
Awall = 10000 Afloor = 46.42 max_volume = 894.43
Awall = 10000 Afloor = 77.43 max_volume = 1926.98
Awall = 10000 Afloor = 129.15 max_volume = 4151.56
Awall = 10000 Afloor = 215.44 max_volume = 8944.27
Awall = 10000 Afloor = 359.38 max_volume = 19269.85
Awall = 10000 Afloor = 599.48 max_volume = 41515.63
Awall = 10000 Afloor = 1000.00 max_volume = 77457.25