Most modern statistical models contain restricted parameters. These include stationarity constraints in time dependent processes, and constraints on the positiveness of variances such as the conditional variances in GARCH models.

Transformations of parameters and penalty methods have been customarily used to enforce constraints in statistical models. Convergence to a solution with these methods, however, has not always been reliable.

Han (1977) proposed the Sequential Quadratic Programming (SQP)
method for the optimization of functions
with general equality and inequality constraints.
This method was applied to a statistical
problem by Jamshidian, et al., (1993).
Software implementations followed:
Matlab's optimization toolbox, SAS's Proc NLP, and Aptech
System's **CML**. **CML** is the
first implementation of the SQP method explicitly for the
maximum likelihood estimation of constrained statistical
models.

Fri Sep 12 09:47:41 PDT 1997