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We extend the constrained maximum likelihood estimation theory for parametersof a completely identified model, proposed by Aitchison and Silvey (1958), toparameters arising from a partially identified model. With a partiallyidentified model, some parameters of the model may only be identified throughconstraints imposed by additional assumptions. We show that, under certainconditions, the constrained maximum likelihood estimator exists and locallymaximize the likelihood function subject to constraints. We then study theasymptotic distribution of the estimator and propose a numerical algorithm forestimating parameters. We also discuss a special situation where exploitingadditional assumptions does not improve estimation efficiency.

The Constrained Maximum Likelihood Estimation For Parameters Arising From Partially Identified Models