  Wavefront phase retrieval from a set of intensity measurements can be
formulated as an optimization problem. Two nonconvex objective models (MLP and
its variants LS) based on maximum likelihood estimation are investigated. We
develop numerical optimization algorithms for real-valued function of complex
variables and apply them to solve the wavefront phase retrieval problem
efficiently. Numerical simulation is given with application to three wavefront
phase retrieval problems. LS model shows better numerical performances than MLP
model. An explanation for this is that the distribution of the eigenvalues of
Hessian matrix of LS model is more clustered than MLP model. LBFGS shows more
robust performance and takes fewer calculations than other line search methods.
