SPSS® 12.0 Command Syntax Reference

Iteration Criteria for CNLR
NLR 1055
The CNLR procedure uses NPSOL (Version 4.0) Fortran Package for Nonlinear Programming
(Gill et al., 1986). The CRITERIA subcommand of CNLR gives the control features of
NPSOL. The following section summarizes the NPSOL documentation.
CNLR uses a sequential quadratic programming algorithm, with a quadratic programming
subproblem to determine the search direction. If constraints or bounds are specified, the first
step is to find a point that is feasible with respect to those constraints. Each major iteration
sets up a quadratic program to find the search direction, p. Minor iterations are used to solve
this subproblem. Then, the major iteration determines a steplength α by a line search, and the
function is evaluated at the new point. An optimal solution is found when the optimality
tolerance criterion is met.
The CRITERIA subcommand has the following keywords when used with CNLR:
ITER n Maximum number of major iterations. Specify any positive integer for
n. The default is max( 50, 3( p+ mL) + 10mN) , where p is the number
of parameters, mL is the number of linear constraints, and mN is the
number of nonlinear constraints. If the search for a solution stops
because this limit is exceeded, CNLR issues a warning message.
MINORITERATION n Maximum number of minor iterations. Specify any positive integer.
This is the number of minor iterations allowed within each major iteration.
The default is max( 50, 3( n + mL+ mN) ) .
CRSHTOL n Crash tolerance. CRSHTOL is used to determine if initial values are
within their specified bounds. Specify any value between 0 and 1. The
default value is 0.01. A constraint of the form a'X≥l is considered a
valid part of the working set if a'X– l <
CRSHTOL( 1 + l ) .
STEPLIMIT n Step limit. The CNLR algorithm does not allow changes in the length
of the parameter vector to exceed a factor of n. The limit prevents very
early steps from going too far from good initial estimates. Specify any
positive value. The default value is 2.
FTOLERANCE n Feasibility tolerance. This is the maximum absolute difference
allowed for both linear and nonlinear constraints for a solution to be
considered feasible. Specify any value greater than 0. The default
value is the square root of your machine’s epsilon.
LFTOLERANCE n Linear feasibility tolerance. If specified, this overrides FTOLERANCE
for linear constraints and bounds. Specify any value greater than 0.
The default value is the square root of your machine’s epsilon.
NFTOLERANCE n Nonlinear feasibility tolerance. If specified, this overrides
FTOLERANCE for nonlinear constraints. Specify any value greater than
0. The default value is the square root of your machine’s epsilon.
LSTOLERANCE n Line search tolerance. This value must be between 0 and 1 (but not
including 1). It controls the accuracy required of the line search that
forms the innermost search loop. The default value, 0.9, specifies an
inaccurate search. This is appropriate for many problems, particularly
if nonlinear constraints are involved. A smaller positive value, corre