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The quantum many-body problem can be rephrased as a variational determinationof the two-body reduced density matrix, subject to a set of N-representabilityconstraints. The mathematical problem has the form of a semidefinite program.We adapt a standard primal-dual interior point algorithm in order to exploitthe specific structure of the physical problem. In particular the matrix-vectorproduct can be calculated very efficiently. We have applied the proposedalgorithm to a pairing-type Hamiltonian and studied the computational aspectsof the method. The standard N-representability conditions perform very well forthis problem.

A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix