  We present a scheme to perform an iterative variational optimization with
infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a
two-dimensional wave function in the thermodynamic limit, to compute the ground
state of a local Hamiltonian. The method is based on a systematic summation of
Hamiltonian contributions using the corner transfer-matrix method. Benchmark
results for challenging problems are presented, including the 2D Heisenberg
model, the Shastry-Sutherland model, and the t-J model, which show that the
variational scheme yields considerably more accurate results than the
previously best imaginary time evolution algorithm, with a similar
computational cost and with a faster convergence towards the ground state.
