function gp

sdpvar h w d

Awall  = 1;
Afloor = 1;

F = set(0.5 < h/w < 2) + set(0.5 < d/w < 2);
F = F + set(2*(h*w+h*d) < Awall) + set(w*d < Afloor);

sol = solvesdp(F,-(h*w*d))

mbg_asserttolequal(sol.problem,0);
mbg_asserttolequal( double(h*w*d),  0.19245008957514, 1e-5);
mbg_asserttolequal( double([h w d]), [ 0.28867519677435   0.57735039354827   1.15470006291485], 1e-3);