The Unconstrained Nonlinear Programming Solver: NLPU Solver Options :: SAS/OR(R) 9.2 User's Guide: Mathematical Programming

The Unconstrained Nonlinear Programming Solver

NLPU Solver Options

The following options are supported by the NLPU solver.

LBFGSCORR=n: specifies the number of Hessian corrections for the L-BFGS algorithms. The value of n can be any integer between 2 and 100. The default value is 7 corrections.

LSARMIJO=

specifies the Armijo parameter $c_1 \in$ (0, 1) for the line-search technique. The default value is 2.0E - 3. See the section "Line-Search Algorithm" for details.

Note: The value of the LSARMIJO= option must be less than the value of the LSWOLFE= option.

LSWOLFE=

specifies the Wolfe parameter $c_2 \in$ (0, 1) for the line-search technique. The default value is 0.7. See the section "Line-Search Algorithm" for details.

Note: The value of the LSWOLFE= option must be greater than the value of the LSARMIJO= option.

LSMAXITER=N

specifies the maximum number of line-search iterations within one L-BFGS or conjugate gradient method. It can also be viewed as the maximum number of function evaluations. The value of N can be any number between 20 and 200. The default value is 200 iterations.

MAXITER=N

specifies that the optimization process stop after a maximum of N iterations. The value of N cannot exceed the largest four-byte, signed integer, which is $2^{31} - 1$ . The default value is 1,000 iterations.

MAXTIME=

specifies an upper limit of

seconds of real time for the optimization process. If you do not specify this option, the procedure does not stop based on the amount of time elapsed. Note that the time specified by the MAXTIME= option is checked only at the end of each iteration. The optimization terminates when the actual running time is greater than or equal to

OPTTOL= $\varepsilon$

specifies the desired tolerance of the relative gradient norm, which is defined as follows:

$\frac{ \vert \nabla\!f(x) \vert _2 }{ \max\,( \vert x\vert _2, 1 ) }, x \in \mathbb{r}^n$

The solver terminates when it finds a point where the relative gradient norm of the objective function is less than $\varepsilon$ . See the section "Conditions of Optimality" for details. The default value of this option is 1.0E - 5.

OBJLIMIT=M

specifies an upper limit on the magnitude of the objective value. For a minimization problem, the algorithm terminates when the objective value becomes less than

; for a maximization problem, the algorithm stops when the objective value exceeds

. When this happens, it implies that either the problem is unbounded or the algorithm diverges. If optimization were allowed to continue, numerical difficulty might be encountered. The default value is

. The minimum acceptable value of

is 1.0E

. If the specified value of

is less than 1.0E

, the value will be reset to the default value 1.0E

PRINTFREQ=j

specifies that the printing of the solution progress to the iteration log should occur after every

iterations. The print frequency,

, is an integer between zero and the largest four-byte, signed integer, which is $2^{31} - 1$ . The value

disables the printing of the progress of the solution. Note that the first and last iterations are also displayed. The default value for this option is 1.

TECH=keyword

TECHNIQUE=keyword

SOLVER=keyword

specifies the optimization technique. Valid keywords are as follows:

FLETREEV
uses the Fletcher-Reeves nonlinear conjugate gradient algorithm. See Fletcher (1987) for details.
LBFGS
uses the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. This is the default solver. See the section "Broyden-Fletcher-Goldfarb-Shanno (BFGS) Algorithm" for details.
POLRIB
uses the Polak-Ribière nonlinear conjugate gradient algorithm. See Fletcher (1987) for details.

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