GAMS — The Solver Manuals - Available Software

536 SNOPT
• t must be a real value in the range 0.0 ≤ t ≤ 1.0.
• The default value t = 0.9 requests just moderate accuracy in the linesearch.
• If the nonlinear functions are cheap to evaluate (this is usually the case for GAMS models), a more
accurate search may be appropriate; try t = 0.1, 0.01 or 0.001. The number of major iterations might
decrease.
• If the nonlinear functions are expensive to evaluate, a less accurate search may be appropriate. In
the case of running under GAMS where all gradients are known, try t = 0.99. (The number of
major iterations might increase, but the total number of function evaluations may decrease enough to
compensate.)
Default: Linesearch tolerance 0.9.
Log frequency k
See Print frequency.
Default: Log frequency 100
LU factor tolerance r 1
LU update tolerance r 2
These tolerances affect the stability and sparsity of the basis factorization B = LU during refactorization
and updating, respectively. They must satisfy r 1 , r 2 ≥ 1.0. The matrix L is a product of matrices of the
form (
1
µ 1
where the multipliers µ satisfy |µ| ≤ r i . Smaller values of r i favor stability, while larger values favor sparsity.
• For large and relatively dense problems, r 1 = 5.0 (say) may give a useful improvement in stability
without impairing sparsity to a serious degree.
• For certain very regular structures (e.g., band matrices) it may be necessary to reduce r 1 and/or r 2 in
order to achieve stability. For example, if the columns of A include a submatrix of the form
⎛
⎜
⎝
)
2 −1
−1 2 −1
−1 2 −1
. .. . .. . ..
both r 1 and r 2 should be in the range 1.0 ≤ r i < 2.0.
,
−1 2 −1
−1 2
Defaults for linear models: LU factor tolerance 100.0 and LU update tolerance 10.0.
The defaults for nonlinear models are LU factor tolerance 3.99 and LU update tolerance 3.99.
LU partial pivoting
LU rook pivoting
LU complete pivoting
The LUSOL factorization implements a Markowitz-type search for pivots that locally minimize the fill-in
subject to a threshold pivoting stability criterion. The rook and complete pivoting options are more
expensive than partial pivoting but are more stable and better at revealing rank, as long as the LU
factor tolerance is not too large (say t 1 < 2.0).
When numerical difficulties are encountered, SNOPT automatically reduces the LU tolerances toward 1.0
and switches (if necessary) to rook or complete pivoting before reverting to the default or specified options
at the next refactorization. (With System information Yes, relevant messages are output to the listing
file.)
Default: LU partial pivoting.
⎞
,
⎟
⎠