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PROC NLP Statement
PROC NLP options^ ;
This statement invokes the NLP procedure. The following options are used with the PROC NLP statement.
ABSCONV= r ABSTOL= r specifies an absolute function convergence criterion. For minimization (maximization), termination requires The default value of ABSCONV is the negative (positive) square root of the largest double precision value.
ABSFCONV= r [ n ] ABSFTOL= r [ n ] specifies an absolute function convergence criterion. For all techniques except NMSIMP, termination requires a small change of the function value in successive iterations:
For the NMSIMP technique the same formula is used, but is defined as the vertex with the lowest function value, and is defined as the vertex with the highest function value in the simplex. The default value is. The optional integer value specifies the number of successive iterations for which the criterion must be satisfied before the process can be terminated.
ABSGCONV= r [ n ] ABSGTOL= r [ n ] specifies the absolute gradient convergence criterion. Termination requires the maximum absolute gradient element to be small:
This criterion is not used by the NMSIMP technique. The default value is =1E-5. The optional integer value specifies the number of successive iterations for which the criterion must be satisfied before the process can be terminated.
ABSXCONV= r [ n ] ABSXTOL= r [ n ] specifies the absolute parameter convergence criterion. For all techniques except NMSIMP, termination requires a small Euclidean distance between successive parameter vectors:
For the NMSIMP technique, termination requires either a small length of the vertices of a restart simplex
or a small simplex size
The NLP Procedure
where the simplex size is defined as the distance of the simplex vertex with the smallest function value to the other simplex points :
The default value is =1E-4 for the COBYLA NMSIMP technique, =1E-8 for the standard NMSIMP technique, and otherwise. The optional integer value specifies the number of successive iterations for which the criterion must be satisfied before the process can be terminated.
ASINGULAR= r ASING= r specifies an absolute singularity criterion for measuring singularity of Hessian and crossproduct Jacobian and their projected forms, which may have to be converted to compute the covariance matrix. The default is the square root of the smallest positive double precision value. For more information, see the "Covariance Matrix" section.
BEST= i produces the i best grid points only. This option not only restricts the output, it also can significantly reduce the computation time needed for sorting the grid point information.
CDIGITS= r specifies the number of accurate digits in nonlinear constraint evaluations. Fractional values such as CDIGITS=4.7 are allowed. The default value is , where is the machine precision. The value of is used to compute the interval length for the computation of finite-difference approximations of the Jacobian matrix of nonlinear constraints.
CLPARM= PL | WALD | BOTH
is similar to but not the same as that used by other SAS procedures. Using CLPARM=BOTH is equivalent to specifying
PROFILE / ALPHA=0.5 0.1 0.05 0.01 OUTTABLE;
The CLPARM=BOTH option specifies that profile confidence limits (PL CLs) for all parameters and for are computed and displayed or written to the OUTEST= data set. Computing the profile confidence limits for all parameters can be very expensive and should be avoided when a difficult optimization problem or one with many parameters is solved. The OUTTABLE option is valid only when an OUTEST= data set is specified in the PROC NLP statement. For CLPARM=BOTH, the table of displayed output contains the Wald confidence limits computed from the standard errors as well as the PL CLs. The Wald confidence limits are not computed (displayed or written to the OUTEST= data set) unless the approximate covariance matrix of parameters is computed.
COV= 1 | 2 | 3 | 4 | 5 | 6 | M | H | J | B | E | U
COVARIANCE= 1 | 2 | 3 | 4 | 5 | 6 | M | H | J | B | E | U
specifies one of six formulas for computing the covariance matrix. For more
FCONV2= r [ n ] FTOL2= r [ n ] specifies another function convergence criterion. For least-squares problems and all techniques except NMSIMP, termination requires a small predicted reduction
of the objective function. The predicted reduction
is based on approximating the objective function by the first two terms of the Taylor series and substituting the Newton step
For the NMSIMP technique, termination requires a small standard deviation of the function values of the simplex vertices ,
where. If there are boundary constraints active
at , the mean and standard deviation are computed only for the unconstrained vertices. The default value is =1E-6 for the NMSIMP technique and the QUANEW technique with nonlinear constraints, and otherwise. The optional integer value specifies the number of successive iterations for which the criterion must be satisfied before the process can be terminated.
FD[=FORWARD | CENTRAL | number ] specifies that all derivatives be computed using finite-difference approximations. The following specifications are permitted: FD=FORWARD uses forward differences. FD=CENTRAL uses central differences. FD= number uses central differences for the initial and final evaluations of the gradient, Jacobian, and Hessian. During iteration, start with forward differences and switch to a corresponding central-difference formula during the iteration process when one of the following two criteria is satisfied: The absolute maximum gradient element is less than or equal to number times the ABSGCONV threshold. The term left of the GCONV criterion is less than or equal to max(1.0E- 6, number × GCONV threshold). The 1.0E-6 ensures that the switch is done, even if you set the GCONV threshold to zero. FD is equivalent to FD=100. Note that the FD and FDHESSIAN options cannot apply at the same time. The
FDHESSIAN option is ignored when only first-order derivatives are used, for example, when the LSQ statement is used and the HESSIAN is not explicitly needed (displayed or written to a data set). For more information, see the "Finite- Difference Approximations of Derivatives" section.
FDHESSIAN[=FORWARD | CENTRAL]
FDHES[=FORWARD | CENTRAL]
FDH[=FORWARD | CENTRAL]
specifies that second-order derivatives be computed using finite-difference approximations based on evaluations of the gradients.
Note that the FD and FDHESSIAN options cannot apply at the same time. For more information, see the "Finite-Difference Approximations of Derivatives" section
FDIGITS= r specifies the number of accurate digits in evaluations of the objective function. Fractional values such as FDIGITS=4.7 are allowed. The default value is , where is the machine precision. The value of is used to compute the interval length for the computation of finite-difference approximations of the derivatives of the objective function and for the default value of the FCONV= option.
FDINT= OBJ | CON | ALL
specifies how the finite-difference intervals should be computed. For FDINT=OBJ, the interval is based on the behavior of the objective function; for FDINT=CON, the interval is based on the behavior of the nonlinear constraints functions; and for FDINT=ALL, the interval is based on the behavior of the objective function and the nonlinear constraints functions. For more information, see the "Finite-Difference Approximations of Derivatives" section.
FSIZE= r specifies the FSIZE parameter of the relative function and relative gradient termination criteria. The default value is. For more details, refer to the FCONV= and GCONV= options.
G4= n is used when the covariance matrix is singular. The value determines which generalized inverse is computed. The default value of is 60. For more information, see the "Covariance Matrix" section.
GCONV= r [ n ] GTOL= r [ n ] specifies the relative gradient convergence criterion. For all techniques except the CONGRA and NMSIMP techniques, termination requires that the normalized predicted function reduction is small:
FDHESSIAN=FORWARD uses forward differences.
FDHESSIAN=CENTRAL uses central differences.
FDHESSIAN uses forward differences for the Hessian except for the initial and final output.
HESCAL=2 specifies the Dennis, Gay, and Welsch (1981) scaling update:
HESCAL=3 specifies that di is reset in each iteration:
where is the relative machine precision. The default value is HESCAL=1 for LEVMAR minimization and HESCAL=0 otherwise. Scaling of the Hessian or crossproduct Jacobian matrix can be time-consuming in the case where general linear constraints are active.
INEST= SAS-data-set INVAR= SAS-data-set ESTDATA= SAS-data-set can be used to specify the initial values of the parameters defined in a DECVAR statement as well as simple boundary constraints and general linear constraints. The INEST= data set can contain additional variables with names corresponding to constants used in the program statements. At the beginning of each run of PROC NLP, the values of the constants are read from the PARMS observation, initializing the constants in the program statements. For more information, see the "INEST= Input Data Set" section.
INFEASIBLE
IFP
specifies that the function values of both feasible and infeasible grid points are to be computed, displayed, and written to the OUTEST= data set, although only the feasible grid points are candidates for the starting point. This option enables you to explore the shape of the objective function of points surrounding the feasible region. For the output, the grid points are sorted first with decreasing values of the maximum constraint violation. Points with the same value of the maximum constraint violation are then sorted with increasing (minimization) or decreasing (maximization) value of the objective function. Using the BEST= option restricts only the number of best grid points in the displayed output, not those in the data set. The INFEASIBLE option affects both the displayed output and the output saved to the OUTEST= data set. The OUTGRID option can be used to write the grid points and their function values to an OUTEST= data set. After small modifications (deleting unneeded information), this data set can be used with the G3D procedure of SAS/GRAPH to generate a three-dimensional surface plot of the objective function depending on two selected parameters. For more information on grids, see the "DECVAR Statement" section.
INHESSIAN[= r ] INHESS[= r ] specifies how the initial estimate of the approximate Hessian is defined for the quasi-Newton techniques QUANEW, DBLDOG, and HYQUAN. There are two alternatives: The specification is not used: the initial estimate of the approximate Hessian is set to the true Hessian or crossproduct Jacobian at. The specification is used: the initial estimate of the approximate Hessian
is set to the multiple of the identity matrix. By default, if INHESSIAN= is not specified, the initial estimate of the approximate Hessian is set to the multiple of the identity matrix , where the scalar is computed from the magnitude of the initial gradient. For most applications, this is a sufficiently good first approximation.
INITIAL= r specifies a value as the common initial value for all parameters for which no other initial value assignments by the DECVAR statement or an INEST= data set are made.
INQUAD= SAS-data-set can be used to specify (the nonzero elements of) the matrix , the vector , and the scalar of a quadratic programming problem,.
This option cannot be used together with the NLINCON statement. Two forms ( dense and sparse ) of the INQUAD= data set can be used. For more information, see the "INQUAD= Input Data Set" section.
INSTEP= r For highly nonlinear objective functions, such as the EXP function, the default initial radius of the trust region algorithms TRUREG, DBLDOG, or LEVMAR or the default step length of the line-search algorithms can result in arithmetic overflows. If this occurs, decreasing values of should be specified, such as INSTEP=1E-1, INSTEP=1E-2, INSTEP=1E-4, and so on, until the iteration starts successfully. For trust region algorithms (TRUREG, DBLDOG, LEVMAR), the INSTEP= option specifies a factor for the initial radius of the trust region. The default initial trust region radius is the length of the scaled gradient. This step corresponds to the default radius factor of. For line-search algorithms (NEWRAP, CONGRA, QUANEW, HYQUAN), the INSTEP= option specifies an upper bound for the initial step length for the line search during the first five iterations. The default initial step length is . For the Nelder-Mead simplex algorithm (NMSIMP), the INSTEP= option defines the size of the initial simplex. For more details, see the "Computational Problems" section.
LCDEACT= r LCD= r specifies a threshold for the Lagrange multiplier that decides whether an active inequality constraint remains active or can be deactivated. For a maximization (minimization), an active inequality constraint can be deactivated only if its Lagrange multiplier is greater (less) than the threshold value. For maximization, must be greater than zero; for minimization, must be smaller than zero. The default value is
where the stands for maximization, the for minimization, ABSGCONV is the value of the absolute gradient criterion, and is the maximum absolute element of the (projected) gradient or.
LCEPSILON= r
for linear approximation. LIS= specifies the Armijo line-search technique (Polak 1971), which uses only function values for linear approximation.
LIST
displays the model program and variable lists. The LIST option is a debugging feature and is not normally needed. This output is not included in either the default output or the output specified by the PALL option.
LISTCODE
displays the derivative tables and the compiled program code. The LISTCODE option is a debugging feature and is not normally needed. This output is not included in either the default output or the output specified by the PALL option. The option is similar to that used in MODEL procedure in SAS/ETS software.
LSPRECISION= r LSP= r specifies the degree of accuracy that should be obtained by the line-search algorithms LIS=2 and LIS=3. Usually an imprecise line search is inexpensive and sufficient for convergence to the optimum. For difficult optimization problems, a more precise and expensive line search may be necessary (Fletcher 1987). The second (default for NEWRAP, QUANEW, and CONGRA) and third line-search methods approach exact line search for small LSPRECISION= values. In the presence of numerical problems, it is advised to decrease the LSPRECISION= value to obtain a more precise line search. The default values are as follows:
For more details, refer to Fletcher (1987).
MAXFUNC= i MAXFU= i specifies the maximum number of function calls in the optimization process. The default values are TRUREG, LEVMAR, NRRIDG, NEWRAP: 125 QUANEW, HYQUAN, DBLDOG: 500 CONGRA, QUADAS: 1000 NMSIMP: 3000 Note that the optimization can be terminated only after completing a full iteration. Therefore, the number of function calls that are actually performed can exceed the number that is specified by the MAXFUNC= option.
MAXITER= i [ n ]
TECH= UPDATE= LSP default
QUANEW DBFGS, BFGS = 0.
QUANEW DDFP, DFP = 0.
HYQUAN DBFGS = 0.
HYQUAN DDFP = 0.
CONGRA all = 0.
NEWRAP no update = 0.
MAXIT= i [ n ] specifies the maximum number of iterations in the optimization process. The default values are: TRUREG, LEVMAR, NRRIDG, NEWRAP: 50 QUANEW, HYQUAN, DBLDOG: 200 CONGRA, QUADAS: 400 NMSIMP: 1000 This default value is valid also when is specified as a missing value. The optional second value is valid only for TECH=QUANEW with nonlinear constraints. It specifies an upper bound for the number of iterations of an algorithm used to reduce the violation of nonlinear constraints at a starting point. The default value is .
MAXSTEP= r [ n ] specifies an upper bound for the step length of the line-search algorithms during the first iterations. By default, is the largest double precision value and is the largest integer available. Setting this option can increase the speed of convergence for TECH=CONGRA, TECH=QUANEW, TECH=HYQUAN, and TECH=NEWRAP.
MAXTIME= r specifies an upper limit of seconds of CPU time for the optimization process. The default value is the largest floating point double representation of the computer. Note that the time specified by the MAXTIME= option is checked only once at the end of each iteration. Therefore, the actual running time of the PROC NLP job may be longer than that specified by the MAXTIME= option. The actual running time includes the rest of the time needed to finish the iteration, time for the output of the (temporary) results, and (if required) the time for saving the results in an OUTEST= data set. Using the MAXTIME= option with a permanent OUTEST= data set enables you to separate large optimization problems into a series of smaller problems that need smaller amounts of CPU time.
MINITER= i MINIT= i specifies the minimum number of iterations. The default value is zero. If more iterations than are actually needed are requested for convergence to a stationary point, the optimization algorithms can behave strangely. For example, the effect of rounding errors can prevent the algorithm from continuing for the required number of iterations.
MODEL= model-name, model-list MOD= model-name, model-list MODFILE= model-name, model-list reads the program statements from one or more input model files created by previous PROC NLP steps using the OUTMODEL= option. If it is necessary to include the program code at a special location in newly written code, the INCLUDE statement can be used instead of using the MODEL= option. Using both the MODEL= option and the INCLUDE statement with the same model file will include the same model twice, which can produce different results than including it once. The MODEL= option is similar to the option used in PROC MODEL in SAS/ETS software.
MSINGULAR= r MSING= r
OUTDER=2, first- and second-order derivatives are written to the data set; for OUTDER=1, only first-order derivatives are written; for OUTDER=0, no derivatives are written to the data set. The default value is OUTDER=0. Derivatives are evaluated at.
OUTEST= SAS-data-set OUTVAR= SAS-data-set creates an output data set that contains the results of the optimization. This is useful for reporting and for restarting the optimization in a subsequent execution of the procedure. Information in the data set can include parameter estimates, gradient values, constraint information, Lagrangian values, Hessian values, Jacobian values, covariance, standard errors, and confidence intervals.
OUTGRID
writes the grid points and their function values to the OUTEST= data set. By default, only the feasible grid points are saved; however, if the INFEASIBLE option is specified, all feasible and infeasible grid points are saved. Note that the BEST= option does not affect the output of grid points to the OUTEST= data set. For more information on grids, see the "DECVAR Statement" section.
OUTHESSIAN
OUTHES
writes the Hessian matrix of the objective function to the OUTEST= data set. If the Hessian matrix is computed for some other reason (if, for example, the PHESSIAN option is specified), the OUTHESSIAN option is set by default.
OUTITER
writes during each iteration the parameter estimates, the value of the objective function, the gradient (if available), and (if OUTTIME is specified) the time in seconds from the start of the optimization to the OUTEST= data set.
OUTJAC
writes the Jacobian matrix of the functions composing the least-squares function to the OUTEST= data set. If the PJACOBI option is specified, the OUTJAC option is set by default.
OUTMODEL= model-name OUTMOD= model-name OUTM= model-name specifies the name of an output model file to which the program statements are to be written. The program statements of this file can be included into the program statements of a succeeding PROC NLP run using the MODEL= option or the INCLUDE program statement. The OUTMODEL= option is similar to the option used in PROC MODEL in SAS/ETS software. Note that the following statements are not part of the program code that is written to an OUTMODEL= data set: MIN, MAX, LSQ, MINQUAD, MAXQUAD, DECVAR, BOUNDS, BY, CRPJAC, GRADIENT, HESSIAN, JACNLC, JACOBIAN, LABEL, LINCON, MATRIX, and NLINCON.
OUTNLCJAC
If an OUTEST= data set is specified, the Jacobian matrix of the nonlinear constraint functions specified by the NLINCON statement is written to the OUTEST= data set. If the Jacobian matrix of the nonlinear constraint functions is computed for some other reason (if, for example, the PNLCJAC option is
specified), the OUTNLCJAC option is set by default.
OUTTIME
is used if an OUTEST= data set is specified and if the OUTITER option is specified. If OUTTIME is specified, the time in seconds from the start of the optimization to the start of each iteration is written to the OUTEST= data set.
PALL
ALL
displays all optional output except the output generated by the PSTDERR, PCOV, LIST, or LISTCODE option.
PCOV
displays the covariance matrix specified by the COV= option. The PCOV option is set automatically if the PALL and COV= options are set.
PCRPJAC
PJTJ
displays the crossproduct Jacobian matrix. If the PALL option is specified and the LSQ statement is used, this option is set automatically. If general linear constraints are active at the solution, the projected crossproduct Jacobian matrix is also displayed.
PEIGVAL
displays the distribution of eigenvalues if a G4 inverse is computed for the covariance matrix. The PEIGVAL option is useful for observing which eigenvalues of the matrix are recognized as zero eigenvalues when the generalized inverse is computed, and it is the basis for setting the COVSING= option in a subsequent execution of PROC NLP. For more information, see the "Covariance Matrix" section.
PERROR
specifies additional output for such applications where the program code for objective function or nonlinear constraints cannot be evaluated during the iteration process. The PERROR option is set by default during the evaluations at the starting point but not during the optimization process.
PFUNCTION
displays the values of all functions specified in a LSQ, MIN, or MAX statement for each observation read fom the DATA= input data set. The PALL option sets the PFUNCTION option automatically.
PGRID
displays the function values from the grid search. For more information on grids, see the "DECVAR Statement" section.
PHESSIAN
PHES
displays the Hessian matrix. If the PALL option is specified and the MIN or MAX statement is used, this option is set automatically. If general linear constraints are active at the solution, the projected Hessian matrix is also displayed.
PHISTORY
time: total running time total time for the evaluation of objective function, nonlinear constraints, and derivatives: shows the total time spent executing the programming statements specifying the objective function, derivatives, and nonlinear constraints, and (if necessary) their first- and second-order derivatives. This is the total time needed for code evaluation before, during, and after iterating. total time for optimization: shows the total time spent iterating. time for some CMP parsing: shows the time needed for parsing the program statements and its derivatives. In most applications this is a negligible number, but for applications that contain ARRAY statements or DO loops or use an optimization technique with analytic second-order derivatives, it can be considerable.
RANDOM= i specifies a positive integer as a seed value for the pseudorandom number generator. Pseudorandom numbers are used as the initial value.
RESTART= i REST= i specifies that the QUANEW, HYQUAN, or CONGRA algorithm is restarted with a steepest descent/ascent search direction after at most iterations. Default values are as follows: CONGRA with UPDATE=PB: restart is done automatically so specification of is not used CONGRA with UPDATE PB: , where is the number of parameters QUANEW, HYQUAN: is the largest integer available
SIGSQ= sq specifies a scalar factor for computing the covariance matrix. If the SIGSQ= option is specified, VARDEF=N is the default. For more information, see the "Covariance Matrix" section.
SINGULAR= r SING= r specifies the singularity criterion for the inversion of the Hessian matrix and crossproduct Jacobian. The default value is 1E-8. For more information, refer to the MSINGULAR= and VSINGULAR= options.
TECH= name TECHNIQUE= name specifies the optimization technique. Valid values for it are as follows:
CONGRA chooses one of four different conjugate gradient optimization algorithms, which can be more precisely specified with the UPDATE= option and modified with the LINESEARCH= option. When this option is selected, UPDATE=PB by default. For , CONGRA is the default optimization technique.
DBLDOG
performs a version of double dogleg optimization, which can be more precisely specified with the UPDATE= option. When this option is selected, UPDATE=DBFGS by default. HYQUAN chooses one of three different hybrid quasi-Newton optimization algorithms which can be more precisely defined with the VERSION= option and modified with the LINESEARCH= option. By default, VERSION=2 and UPDATE=DBFGS. LEVMAR performs the Levenberg-Marquardt minimization. For , this is the default minimization technique for least-squares problems. LICOMP solves a quadratic program as a linear complementarity problem. NMSIMP performs the Nelder-Mead simplex optimization method. NONE does not perform any optimization. This option can be used to do grid search without optimization to compute and display derivatives and covariance matrices which cannot be obtained efficiently with any of the optimization techniques NEWRAP performs the Newton-Raphson optimization technique. The algorithm combines a line-search algorithm with ridging. The line-search algorithm LINESEARCH=2 is the default. NRRIDG performs the Newton-Raphson optimization technique. For and non- linear least-squares, this is the default. QUADAS performs a special quadratic version of the active set strategy. QUANEW chooses one of four quasi-Newton optimization algorithms which can be defined more precisely with the UPDATE= option and modified with the LINESEARCH= option. This is the default for or if there are nonlinear constraints. TRUREG performs the trust region optimization technique.
UPDATE= method UPD= method specifies the update method for the (dual) quasi-Newton, double dogleg, hybrid quasi-Newton, or conjugate gradient optimization technique. Not every update method can be used with each optimizer. For more information, see the "Optimization Algorithms" section. Valid values for method are as follows:
BFGS
performs the original BFGS (Broyden, Fletcher, Goldfarb, & Shanno) update of the inverse Hessian matrix.
DBFGS
performs the dual BFGS (Broyden, Fletcher, Goldfarb, & Shanno) update of the Cholesky factor of the Hessian matrix.
converted to compute the covariance matrix. The default value is 1E-8 if the SINGULAR= option is not specified and the value of SINGULAR otherwise. For more information, see the "Covariance Matrix" section.
XCONV= r [ n ] XTOL= r [ n ] specifies the relative parameter convergence criterion. For all techniques except NMSIMP, termination requires a small relative parameter change in subsequent iterations:
For the NMSIMP technique, the same formula is used, but is defined as the
vertex with the lowest function value and is defined as the vertex with the
highest function value in the simplex. The default value is =1E-8 for the NMSIMP technique and otherwise. The optional integer value specifies the number of successive iterations for which the criterion must be satisfied before the process can be terminated.
XSIZE= r specifies the parameter of the relative parameter termination criterion. The default value is. For more details, see the XCONV= option.
Copyright © 2004 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
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