Description

The number of factorizations since the start of the run.

A code giving the reason for the present factorization.

The current iteration number.

The current number of infeasibilities.

 If Infeas > 0, this is the current sum of infeasibilities.
 If Infeas = 0, it is the current QP objective function.

The number of nonlinear variables in the current basis B (not printed if B_S is factorized).

The number of linear variables in B (not printed if B_S is factorized).

The number of slack variables in B (not printed if B_S is factorized).

The number of nonzero matrix elements in B.  (not printed if B_S  is factorized).

The percentage nonzero density of B, 100 x Elems/(m²), where m is the number of rows in the problem (m = Nonlinear + Linear + Slacks).

The number of times the data structure holding the partially factored matrix needed to be compressed to recover unused storage.  Ideally this number should be zero.  If it is more than 3 or 4, the amount of workspace available to SNOPT should be increased for efficiency.

The average Markowitz merit count for the elements chosen to be the diagonals of PUQ.  Each merit count is defined to be (c-1)(r-1) where c and r are the number of nonzeros in the column and row containing the element at the time it is selected to be the next diagonal.  Merit is the average of m such quantities.  It gives an indication of how much work was required to preserve sparsity during the factorization.

The number of nonzeros in L.  On most machines, each nonzero is represented by one 8-byte real and two 4-byte integer data types.

The number of nonzeros in U.  The storage required for each nonzero is the same as for the nonzeros of L.

The percentage increase in the number of nonzeros in L and U relative to the number of nonzeros in B;  i.e.,
                100 x (lenL + lenU - Elems)/Elems.

is m, the number of rows in the problem. Note that
                m = Ut + Lt + bp.

is the number of triangular rows of B  at the top of U.

is the number of columns remaining when the density of the basis matrix being factorized reached 0.3.

The maximum subdiagonal element in the columns of L.  This will be no larger than the LU factor tolerance.

The maximum nonzero element in B.

The maximum nonzero element in U, excluding elements of B that remain in U  unaltered.  (For example, if a slack variable is in the basis, the corresponding row of B  will become a row of U  without alteration.  Elements in such rows will not contribute to Umax.  If the basis is strictly triangular, none of the elements of B  will contribute, and Umax will be zero.)

Ideally, Umax should not be substantially larger than  Bmax.  If it is several orders of magnitude larger, it may be advisable to reduce the LU factor tolerance to some value nearer 1.0.

Umax is  not printed if B_S  is factorized.

The smallest diagonal element of PUQ in absolute magnitude.

The ratio Umax/Bmax, which should not be too large (see above).

As long as Lmax is not large (say 10.0 or less, max{Bmax,Umax}/Umin gives an estimate of the condition number of B.  If this number is extremely large, the basis is nearly singular and some numerical difficulties might occur.  (However, an effort is made to avoid near-singularity by using slacks to replace columns of B that would have made Umin extremely small.  Messages are issued to this effect, and the modified basis is refactored.)

is the number of triangular columns of B at the left of L.

is the size of the "bump'' or block to be factorized nontrivially after the triangular rows and columns of B have been removed.

is the number of columns remaining when the density of the basis matrix being factorized reached 0.6.