COMT vs. OPMT vs. MLMT vs. CMLMT

What are the differences between COMT vs. OPMT vs. MLMT vs. CMLMT?

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OPMT optimizes an objective function allowing for bounds on parameters, but no other constraints on parameters.
COMT optimizes an objective function subject to general constraints on parameters, linear or nonlinear, equality or inequality, as well as bounds.
MLMT is like OPMT except that it knows about datasets and optimizes a log-likelihood objective function, that is, it produces maximum likelihood estimates.  It also provides for a variety of types of statistical inference.
CMLMT (also known as CMMT) is like COMT except that it knows about datasets  and optimizes a log-likelihood objective function, that is, it produces maximum likelihood estimates.  It also provides for a variety of types of statistical inference.

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OPMT optimizes an objective function allowing for bounds on parameters, but no other constraints on parameters.
COMT optimizes an objective function subject to general constraints on parameters, linear or nonlinear, equality or inequality, as well as bounds.
MLMT is like OPMT except that it knows about datasets and optimizes a log-likelihood objective function, that is, it produces maximum likelihood estimates.  It also provides for a variety of types of statistical inference.
CMLMT (also known as CMMT) is like COMT except that it knows about datasets  and optimizes a log-likelihood objective function, that is, it produces maximum likelihood estimates.  It also provides for a variety of types of statistical inference.

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