The overdetermination of the mathematical problem underlying ptychography is reduced by a host of experimentally more desirable settings. Furthermore, reconstruction of the sample-induced phase shift is typically limited by uncertainty in the experimental parameters and finite sample thicknesses. Presented is a conjugate gradient descent algorithm, regularized optimization for ptychography (ROP), that recovers the partially known experimental parameters along with the phase shift, improves resolution by incorporating the multislice formalism to treat finite sample thicknesses, and includes regularization in the optimization process, thus achieving reliable results from noisy data with severely reduced and underdetermined information.