% Boyd, Kim, Vandenberghe, and Hassibi, "A Tutorial on Geometric Programming"
% Written for CVX by Almir Mutapcic 02/08/06
% (a figure is generated)
%
% Maximizes volume of a box-shaped structure which has constraints
% on its total wall area, its total floor area, and which has lower
% and upper bounds on the aspect ratios. This leads to a GP:
%
%   maximize   h*w*d
%       s.t.   2(h*w + h*d) <= Awall, w*d <= Afloor
%              alpha <= h/w <= beta
%              gamma <= d/w <= delta
%
% where variables are the box height h, width w, and depth d.

% problem constants
alpha = 0.5; beta = 2; gamma = 0.5; delta = 2;

% varying parameters for an optimal trade-off curve
N = 10;
Afloor = logspace(1,3,N);
Awall  = [100 1000 10000];
opt_volumes = zeros(length(Awall),N);

disp('Computing optimal box volume for:')

% setup various GP problems with varying parameters
for k = 1:length(Awall)
  Awall_k = Awall(k);
  fprintf( 'Awall = %d:\n', Awall(k) );
  for n = 1:N
    % resolve the problem with varying parameters
    Afloor_n = Afloor(n);
    fprintf( '    Afloor = %7.2f: ', Afloor(n) );
    cvx_begin gp quiet
      variables h w d
      % objective function is the box volume
      maximize( h*w*d )
      subject to
        2*(h*w + h*d) <= Awall_k;
        w*d <= Afloor_n;
        alpha <= h/w <= beta;
        gamma <= d/w <= delta;
    cvx_end
    fprintf( 'max_volume = %3.2f\n', cvx_optval );
    opt_volumes(k,n) = cvx_optval;
  end
end

% plot the tradeoff curve
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
    Afloor =   16.68: max_volume = 102.11
    Afloor =   27.83: max_volume = 131.87
    Afloor =   46.42: max_volume = 170.32
    Afloor =   77.43: max_volume = 192.45
    Afloor =  129.15: max_volume = 192.45
    Afloor =  215.44: max_volume = 192.45
    Afloor =  359.38: max_volume = 192.45
    Afloor =  599.48: max_volume = 192.45
    Afloor = 1000.00: max_volume = 192.45
Awall = 1000:
    Afloor =   10.00: max_volume = 89.44
    Afloor =   16.68: max_volume = 192.70
    Afloor =   27.83: max_volume = 415.16
    Afloor =   46.42: max_volume = 894.43
    Afloor =   77.43: max_volume = 1926.98
    Afloor =  129.15: max_volume = 2841.16
    Afloor =  215.44: max_volume = 3669.50
    Afloor =  359.38: max_volume = 4739.34
    Afloor =  599.48: max_volume = 5998.71
    Afloor = 1000.00: max_volume = 6085.81
Awall = 10000:
    Afloor =   10.00: max_volume = 89.44
    Afloor =   16.68: max_volume = 192.70
    Afloor =   27.83: max_volume = 415.16
    Afloor =   46.42: max_volume = 894.43
    Afloor =   77.43: max_volume = 1926.98
    Afloor =  129.15: max_volume = 4151.56
    Afloor =  215.44: max_volume = 8944.27
    Afloor =  359.38: max_volume = 19269.85
    Afloor =  599.48: max_volume = 41515.63
    Afloor = 1000.00: max_volume = 77459.67