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

600 APPENDIX F. MOSEK FILE FORMATS
F.2.1.1
The objective
The first section beginning with one of the keywords
max
maximum
maximize
min
minimum
minimize
defines the objective sense and the objective function, i.e.
The objective may be given a name by writing
myname:
c T x + 1 2 xT Q o x.
before the expressions. If no name is given, then the objective is named obj.
The objective function contains linear and quadratic terms. The linear terms are written as
4 x1 + x2 - 0.1 x3
and so forth. The quadratic terms are written in square brackets ([]) and are either squared or
multiplied as in the examples
x1^2
and
x1 * x2
There may be zero or more pairs of brackets containing quadratic expressions.
An example of an objective section is:
minimize
myobj: 4 x1 + x2 - 0.1 x3 + [ x1^2 + 2.1 x1 * x2 ]/2
Please note that the quadratic expressions are multiplied with 1 2
, so that the above expression means
minimize 4x 1 + x 2 − 0.1 · x 3 + 1 2 (x2 1 + 2.1 · x 1 · x 2 )
If the same variable occurs more than once in the linear part, the coefficients are added, so that 4 x1
+ 2 x1 is equivalent to 6 x1. In the quadratic expressions x1 * x2 is equivalent to x2 * x1 and as
in the linear part , if the same variables multiplied or squared occur several times their coefficients are
added.
F.2.1.2
The constraints
The second section beginning with one of the keywords
subj to
subject to
s.t.