  We adapt and optimize the projected-pair-entangled-state (PEPS) algorithm on
finite lattices (fPEPS) for two-dimensional Hubbard models and apply the
algorithm to the Hubbard model with nearest-neighbor hopping on a square
lattice. In particular, we formulate the PEPS algorithm using projected
entangled pair operators, incorporate SU(2) symmetry in all tensor indices, and
optimize the PEPS using both iterative-diagonalization-based local bond
optimization and gradient-based optimization of the PEPS. We discuss the
performance and convergence of the algorithm for the Hubbard model on lattice
sizes of up to 8x8 for PEPS states with U(1) symmetric bond dimensions of up to
D = 8 and SU(2) symmetric bond dimensions of up to D = 6. Finally, we comment
on the relative and overall efficiency of schemes for optimizing fPEPS.
