MOLPRO

45 MINIMIZATION OF FUNCTIONS 340
45 MINIMIZATION OF FUNCTIONS
The minimization of general functions of one or more variables can be carried out using the
command:
MINIMIZE, func, x 1 [, x 2 , x 3 , . . . ]
where func represents a function of up to 50 variables x 1 , x 2 , . . . . Two different optimization
methods can be selected as described below which do or do not use numerical derivative information.
The optimization method, as well as finer control over func, can be chosen using the METHOD
directive
METHOD, key [, key1=value, key2=value, . . . ]
where key defines the optimization method. Valid options for key are:
BFGS
SIMPLEX
Broyden-Fletcher-Goldfarb-Shanno conjugate gradient method, which
uses numerical gradients (default)
Downhill simplex method, which uses only function evaluations
Options to these methods, key1, key2, . . . , are:
VARSCALE=vscale
THRESH=thresh
VSTEP=epsd
PROC=procname
STARTCMD=command
Optimization in space of scaled variables.
vscale=0 no scaling (not recommended)
vscale=1 optimization in the space of ln(x)
vscale=2 optimization in space of initial value scaling, e.g., x 1 /x 1i
(default)
Required accuracy of either the optimized gradient (BFGS) or function
value (SIMPLEX). The default is 1 · 10 −4 .
Step size for numerical gradients (BFGS) or initial SIMPLEX vertices
Specifies the procedure to be executed in each optimization step. This
defines a complete function evaluation (if needed, numerical gradients
will be evaluated using this procedure as well)
Specifies a start command. In each optimization step all input beginning
with command to the current MINIMIZE is processed.
Miscellaneous directives
MAXIT=maxit
maximum number of optimization cycles. The default is 30 for BFGS
and 100 for SIMPLEX.