The MOSEK command line tool Version 7.0 (Revision 141)

60 CHAPTER 7. THE ANALYZERS
7.1.2 Objective
The second part of the survey focuses on (the linear part of) the objective, summarizing the optimization
sense and the coefficients’ absolute value range and distribution. The number of 0 (zero)
coefficients is singled out (if any such variables are in the problem).
The range is displayed using three terms:
min |c|:
The minimum absolute value among all coeffecients
min |c|>0:
The minimum absolute value among the nonzero coefficients
max |c|:
The maximum absolute value among the coefficients
If some of these extrema turn out to be equal, the display is shortened accordingly:
• If min |c| is greater than zero, the min |c|?0 term is obsolete and will not be displayed
• If only one or two different coefficients occur this will be displayed using all and an explicit
listing of the coefficients
The absolute value distribution is displayed as a table summarizing the numbers by orders of magnitude
(with a ratio of 10). Again, the number of variables with a coefficient of 0 (if any) is singled out. Each
line of the table is headed by an interval (half-open intervals including their lower bounds), and is
followed by the number of variables with their objective coefficient in this interval. Intervals with no
elements are skipped.
7.1.3 Linear constraints
The third part of the survey displays information on the nonzero coefficients of the linear constraint
matrix.
Following a brief summary of the matrix dimensions and the number of nonzero coefficients in total,
three sections provide further details on how the nonzero coefficients are distributed by row-wise count
(A i), by column-wise count (A|j), and by absolute value (|A(ij)|). Each section is headed by
a brief display of the distribution’s range (min and max), and for the row/column-wise counts the
corresponding densities are displayed too (in parentheses).
The distribution tables single out three particularly interesting counts: zero, one, and two nonzeros
per row/column; the remaining row/column nonzeros are displayed by orders of magnitude (ratio 2).
For each interval the relative and accumulated relative counts are also displayed.
Note that constraints may have both linear and quadratic terms, but the empty rows and columns
reported in this part of the survey relate to the linear terms only. If empty rows and/or columns are
found in the linear constraint matrix, the problem is analyzed further in order to determine if the