If Minor print level > 0, one line of information is output to the PRINT file every kth minor iteration, where k is the specified Minor print frequency (default k =1). A heading is printed before the first such line following a basis factorization. The heading contains the items described below. In this description, a PRICE operation is defined to be the process by which a nonbasic variable is selected to become superbasic (in addition to those already in the superbasic set). The selected variable is denoted by jq. Variable jq often becomes basic immediately. Otherwise it remains superbasic, unless it reaches its opposite bound and returns to the nonbasic set.
If Partial price is in effect, variable jq is selected from App or Ipp, the ppth segments of the constraint matrix (A - I).
|
Label |
Description |
|
Itn |
The current iteration number. |
|
pp |
The Partial Price indicator. The variable selected by the last PRICE operation came from the ppth partition of A and –I. pp is set to zero when the basis is refactored. |
|
dj |
This is the reduced cost (or reduced gradient) of the variable jq selected by PRICE at the start of the present iteration. Algebraically, dj is dj =gj - pTaj for j = jq, where gj is the gradient of the currentobjective function, p is the vector of dual variables for the QP subproblem, and aj is the jth column of (A - I). Note that dj is the 1-norm of the reduced-gradient vector at the start of the iteration, just after the PRICE operation. |
|
+SBS |
The variable jq selected by PRICE to be added to the superbasic set. |
|
-SBS |
The variable chosen to leave the set of superbasics. It has become basic if the entry under -B is nonzero; otherwise it has become nonbasic. |
|
-BS |
The variable removed from the basis (if any) to become nonbasic. |
|
-B |
The variable removed from the basis (if any) to swap with a slack variable made superbasic by the latest PRICE. The swap is done to ensure that there are no superbasic slacks. |
|
Step |
The step length a taken along the current search direction p. The variables x have just been changed to x +ap. If a variable is made superbasic during the current iteration (+SBS > 0), Step will be the step to the nearest bound. During Phase 2, the step can be greater than one only if the reduced Hessian is not positive definite. |
|
Pivot |
If column aq replaces the rth column of the basis B, Pivot is the rth element of a vector y satisfying By = aq. Wherever possible, Step is chosen to avoid extremely small values of Pivot (since they cause the basis to be nearly singular). In rare cases, it may be necessary to increase the Pivot tolerance to exclude very small elements of y from consideration during the computation of Step . |
|
L |
The number of nonzeros representing the basis factor L. Immediately after a basis factorization B = LU, this is lenL, the number of subdiagonal elements in the columns of a lower triangular matrix. Further nonzeros are added to L when various columns of B are later replaced. (Thus, L increases monotonically.) |
|
U |
The number of nonzeros in the basis factor U. Immediately after a basis factorization, this is lenU, the number of diagonal and superdiagonal elements in the rows of an upper-triangular matrix. As columns of B are replaced, the matrix U is maintained explicitly (in sparse form). The value of U may fluctuate up or down; in general it will tend to increase. |
|
ncp |
The number of compressions required to recover storage in the data structure for U. This includes the number of compressions needed during the previous basis factorization. Normally ncp should increase very slowly. If not, the amount of integer and real workspace available to SNOPT should be increased by a significant amount. As a suggestion, the work arrays iw(*) and rw(*) should be extended by L + U elements. |
|
nInf |
The number of infeasibilities after the present iteration. This number will not increase unless the iterations are in elastic mode. |
|
Sinf,Objective |
If nInf > 0, this is sInf, the sum of infeasibilities after the present iteration. It usually decreases at each nonzero Step, but if nInf decreases by 2 or more, sInf may occasionally increase. In elastic mode, the heading is changed to Composite Obj, and the value printed decreases monotonically. If nInf = 0, the value printed is Objective, the QP objective function after the present iteration. |
The following items are printed if the problem is nonlinear or if the superbasic set is non-empty (i.e., if the current solution is nonbasic).
|
Label |
Description |
|
Norm rg |
The norm of the reduced-gradient vector at the start of the iteration. (It is the norm of the vector with elements dj for variables j in the superbasic set.) During Phase 2 this norm will be approximately zero after a unit step. |
|
nS |
The current number of superbasic variables. |
|
cond Hz |
See the major iteration log. |