The MOSEK Python optimizer API manual Version 7.0 (Revision 141)

13.2. ANALYZING INFEASIBLE PROBLEMS 167
corresponding constraints have any quadratic terms or the corresponding variables are used in conic
or quadratic constraints; cf. the last two examples of appendix G.
The distribution of the absolute values, |A(ij)|, is displayed just as for the objective coefficients
described above.
13.1.4 Constraint and variable bounds
The fourth part of the survey displays distributions for the absolute values of the finite lower and upper
bounds for both constraints and variables. The number of bounds at 0 is singled out and, otherwise,
displayed by orders of magnitude (with a ratio of 10).
13.1.5 Quadratic constraints
The fifth part of the survey displays distributions for the nonzero elements in the gradient of the
quadratic constraints, i.e. the nonzero row counts for the column vectors Qx . The table is similar to
the tables for the linear constraints’ nonzero row and column counts described in the survey’s third
part.
Note: Quadratic constraints may also have a linear part, but that will be included in the linear
constraints survey; this means that if a problem has one or more pure quadratic constraints, part three
of the survey will report an equal number of linear constraint rows with 0 (zero) nonzeros, cf. the last
example in appendix G. Likewise, variables that appear in quadratic terms only will be reported as
empty columns (0 nonzeros) in the linear constraint report.
13.1.6 Conic constraints
The last part of the survey summarizes the model’s conic constraints. For each of the two types of
cones, quadratic and rotated quadratic, the total number of cones are reported, and the distribution
of the cones’ dimensions are displayed using intervals. Cone dimensions of 2, 3, and 4 are singled out.
13.2 Analyzing infeasible problems
When developing and implementing a new optimization model, the first attempts will often be either
infeasible, due to specification of inconsistent constraints, or unbounded, if important constraints have
been left out.
In this chapter we will
• go over an example demonstrating how to locate infeasible constraints using the MOSEK infeasibility
report tool,
• discuss in more general terms which properties that may cause infeasibilities, and
• present the more formal theory of infeasible and unbounded problems.