CMA Research Report
MRR02-002
Z.F. Li, M.R. Osborne and T. Prvan
Numerical algorithms for constrained maximum likelihood estimation
Abstract:
This paper describes an algorithm for solving constrained maximum
likelihood estimation that incorporates a number of novel features. This new
algorithm is a SQP type method, we call it MLESOL. MLESOL maintains the use of an
estimate of Fischer information matrix to the Hessian of the negative
log-likelihood but also encompasses a secant approximation S to
the second-order part of the augmented Lagrangian function along with
tests for when to use this information. S is sized before
updating. The local quadratic model used has a form something like that of
Tapia's SQP augmented scale BFGS secant method but exploring the
additional structure of the problem. The step choice algorithm is based on
minimizing a local quadratic model subject to the linearized constraints
and an elliptical trust region centered at the current approximate
minimizer. This is accomplished using the approach of Byrd and Omojokun
trust region, together with a special module for assessing the quality of
the step thus computed. The numerical performance of Algorithm MLESOL is
studied by means of an example involving the estimation of a mixture
density.
AMS Classification:
65L10
Date:
21 January 2002
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