The problem of finding a minimum energy state (or density matrix) can be restated as a linear programming problem. This problem can be solved sequentially applying the maximum entropy principle, using the energy as a control parameter. The method thus described falls within the class of interior point methods for linear programs. In the classical (non quantum) setup, things go pretty much as expected, whereas in the quantum setup the approach depends on whether we use a basis in which the density matrix is diagonal or not. Here we present a novel maxentropic way of solving this problem.