Printed Output

The NLP Procedure

Printed Output

Procedure Initialization

After the procedure has processed the problem it prints summary information about the problem and the options that you have selected. It may also print a list of linearly dependent constraints and other information about the constraints and parameters.

Optimization Start

At the start of optimization the procedure prints

the number of constraints that are active at the starting point, or more precisely, the number of constraints that are currently members of the working set. If this number is followed by a plus sign, there are more active constraints, of which at least one is temporarily released from the working set due to negative Lagrange multipliers.
The value of the objective function at the starting point.
If the (projected) gradient is available, the value of the largest absolute (projected) gradient element.
For the TRUREG and LEVMAR subroutines, the initial radius of the trust region around the starting point.

Iteration History

In general, the iteration history consists of one line of printed output containing the most important information for each iteration. The iteration-extensive Nelder-Mead simplex method, however, prints only one line for several internal iterations. This technique skips the output for some iterations because:

Some of the termination tests (size and standard deviation) are rather time-consuming compared to the simplex operations, and are only done every five simplex operations.
The resulting history output is smaller.

The _LIST_ variable (see Program Statements in the Syntax section) also allows the user to print the parameter estimates x^(k) and the gradient g^(k) in all or some selected iterations k.

The iteration history always includes the following (the words in parentheses indicate the column header output):

the iteration number (iter)
the number of iteration restarts (nrest)
the number of function calls (nfun)
the number of active constraints (act)
the value of the optimization criterion (optcrit)
the difference between adjacent function values (difcrit)
the maximum of the absolute (projected) gradient components (maxgrad)

An apostrophe trailing the number of active constraints indicates that at least one of the active constraints was released from the active set due to a significant Lagrange multiplier.

The optimization history is printed by default because it is important to check for possible convergence problems.

Optimization Termination

The output of the optimization history ends with a short output of information concerning the optimization result:

The number of constraints that are active at the final point, or more precisely, the number of constraints that are currently members of the working set. When this number is followed by a plus sign, it indicates that there are more active constraints of which at least one is temporarily released from the working set due to negative Lagrange multipliers.
The value of the objective function at the final point.
If the (projected) gradient is available, the value of the largest absolute (projected) gradient element.
Other information that is specific for the optimization technique.

The NOPRINT option suppresses all printed output to the list file and only ERROR's, WARNING's, and NOTE's are printed to the log file. The PALL option sets a large group of some of the commonly used specific print options, the PSHORT option suppresses some, and the PSUM (or PSUMMARY) option suppresses almost all of the default output. The following table summarizes the correspondence between the general and the specific print options:

Output Options	PALL	default	PSHORT	PSUM
	y	y	y	y	summary of optimization
	y	y	y	n	parameter estimates
	y	y	y	n	gradient of objective func
PHISTORY	y	y	y	n	iteration history
PINIT	y	y	n	n	setting of initial values
	y	y	n	n	listing of constraints
PGRID	y	n	n	n	results of grid search
PNLCJAC	y	n	n	n	Jacobian nonlin. constr.
PFUNCTION	y	n	n	n	values of functions
PEIGVAL	y	n	n	n	eigenvalue distribution
PCRPJAC	y	n	n	n	cross-product Jacobian
PHESSIAN	y	n	n	n	Hessian matrix
PSTDERR	y	n	n	n	approx. standard errors
PCOV	y	n	n	n	covariance matrices
PJACOBI	n	n	n	n	Jacobian
LIST	n	n	n	n	model program, variables
LISTCODE	n	n	n	n	compiled model program

Missing Values

Missing Values in Program Statements

There is one very important reason for using missing values in program statements specifying the values of the objective functions and derivatives: it may not be possible to evaluate the program statements for a particular point x. For example, the extrapolation formula of one of the line-search algorithms may generate large x values for which the exp function cannot be evaluated without floating point overflow. The compiler of the program statements may check for such situations automatically, but it would be safer if you check the feasibility of your program statements. In some cases, the specification of boundary or linear constraints for parameters can avoid such situations. In many other cases you can indicate that x is a bad point simply by returning a missing value for the objective function. In such cases the optimization algorithms in PROC NLP shorten the step size $\alpha$ or reduce the trust-region radius so that the next point will be closer to the point which was already successfully evaluated at the last iteration. Note, the starting point x⁽⁰⁾ must be a point for which the program statements can be evaluated.

Missing Values in Input Data Sets

Observations with missing values in the DATA= data set for variables used in the objective function can lead to a missing value of the objective function implying that the corresponding BY group of data is not processed. The NOMISS option can be used to skip those observations of the DATA= data set for which relevant variables have missing values. Relevant are such variables which are referred to in program statements.

There can be different reasons to include observations with missing values in the INEST= data set. The value of the _RHS_ variable is not used in some cases and can be missing. Missing values for the variables corresponding to parameters in the _TYPE_ =:

PARMS observation(s) cause those parameters to have initial values assigned by the PARMS statement, or by the RANDOM= or INITIAL= option.
UPPERBD or LOWERBD observation(s) cause those parameters to be unconstrained by upper or lower bounds.
LE, GE, or EQ observation(s) cause those parameters to have zero values in the constraint.

In gerneral missing values are treated as zeros.

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