Sets starting diagonal OMEGA values for purposes of simulated annealing by NONMEM subroutine CONSTRAINT. This facilitates EM (Expectation Maximization) search methods.

In the above example, initial values of OMEGA(1,1), OMEGA(2,2), OMEGA(3,3), and OMEGA(5,5) are set to 0.3, while initial OMEGA(6,6) and OMEGA(7,7) are set to 1.0.

A number-list may contain a single integer, a range of integers (with "-"), or a series of integers and ranges separated by comma. Required.

A value may be any numeric value. Optional; default is 0.

When $EST CONSTRAIN>=4, an algorithm in subroutine CONSTRAINT will initially set the OMEGAs to these values, and then shrink these OMEGA values more and more with each iteration, and eventually shrinks the OMEGA's to 0, the intended target value for that Omega. This is a technique that may be used especially with SAEM, to provide an annealing method for moving THETAs that have 0 omega values associated with them. The default is the use of gradient methods, which are good for problems starting near the solution, whereas the annealing method is more suitable for problems starting far from the solution.

Subroutine CONSTRAINT obtains values entered via $ANNEAL record in the array OMEGANNL. Any value that is set to 0 in $ANNEAL is given the default value of .3.

This record is optional. If omitted, the starting values of Omega are those specified in the $OMEGA record.

NONMEM's default CONSTRAINT.f90 is identical to Subroutine source/CONSTRAINT.f90.

Consider the following example ("examples/anneal"), for an Emax model in which the Hill coefficient does not have inter-subject variance (its OMEGA is fixed to zero).

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$PROB Emax model with hill=3
$INPUT ID DOSE DV
$DATA anneal.dat IGNORE=@
$PRED
 
 MU_1 = THETA(1)
 EMAX = EXP(MU_1+ETA(1))
 MU_2 = THETA(2)
 ED50 = EXP(MU_2+ETA(2))
 MU_3 = THETA(4)
 E0   = EXP(MU_3+ETA(3))

 MU_4=THETA(3)
 HILL = EXP(MU_4+ETA(4))

 IPRED = E0+EMAX*DOSE**HILL/(ED50**HILL+DOSE**HILL)
 Y     = IPRED + EPS(1)

$THETA  4.1 ; 1. Emax
$THETA  6.9 ; 2. ED50
$THETA  0.001 ; 3. Hill
$THETA  2.3 ; 4. E0

$OMEGA BLOCK(2) 0.1
                 0.01 0.1
$OMEGA 0.1
$OMEGA 0.0 FIXED

$ANNEAL 4:0.3

$SIGMA 1
$ESTIMATION METH=SAEM INTER NBURN=1000 NITER=500 ISAMPLE=5 IACCEPT=0.3 CINTERVAL=25 CTYPE=0 NOABORT PRINT=50 CONSTRAIN=5 SIGL=8
$ESTIMATION METH=IMP INTER PRINT=1 NITER=0 ISAMPLE=10000 EONLY=1 CONSTRAIN=0 MAPITER=0 DF=4
$COV MATRIX=R UNCONDITIONAL

The user may modify the subroutine CONSTRAINT that performs the simulated annealing algorithm. The source code to the CONSTRAINT subroutine is available from the ..\source directory as constraint.f90 , and the user may copy this to their run directory, and as convenient, to rename it. Then, specify OTHER=name_of_source.f90 in the $SUBROUTINE record, as shown in example 9. The subroutine CONSTRAINT may also be used to provide any kind of constraint pattern on any parameters.