Implementation and Applications of a Three-Round User Strategy for Improved Principal Axis Minimization

Keywords

evaluation and improvement of optimization software, extended principal axis minimization, numerical optimization, PRAXIS, psychometrics

Abstract

This paper presents a three-round user strategy (EPM), extending the C implementation of Brent’s PRAXIS algorithm by Gegenfurtner. In a first round, EPM applies a multistart procedure for global optimization, randomly generating and evaluating multiple sets of start values drawn from weighted primary and secondary intervals. Using the parameter estimates of the smallest first round minimum, in a second and third round, EPM performs iterative minimization runs and applies an additional break-off criterion to improve and stabilize the approximated minimum and parameter estimates. Moreover, EPM increases the precision of the original PRAXIS implementation by a conversion from the double to the long double data type. This conversion is not trivial and even seen to be essential for minimizing a complex empirical function from psychometrics. Important special cases of EPM are discussed and promising strategies for the handling of EPM are proposed. EPM’s advantages over PRAXIS are illustrated using two different functions: a ‘well-behaved’ Rosenbrock function and an ‘ill-behaved’ psychometric likelihood function.

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