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

F.2. THE LP FILE FORMAT 599
minimize/maximize
c T x + 1 2 qo (x)
subject to l c ≤ Ax + 1 2 q(x) ≤ uc ,
l x ≤ x ≤ u x ,
x J integer,
where
• x ∈ R n is the vector of decision variables.
• c ∈ R n is the linear term in the objective.
• q o :∈ R n → R is the quadratic term in the objective where
and it is assumed that
q o (x) = x T Q o x
Q o = (Q o ) T .
• A ∈ R m×n is the constraint matrix.
• l c ∈ R m is the lower limit on the activity for the constraints.
• u c ∈ R m is the upper limit on the activity for the constraints.
• l x ∈ R n is the lower limit on the activity for the variables.
• u x ∈ R n is the upper limit on the activity for the variables.
• q : R n → R is a vector of quadratic functions. Hence,
where it is assumed that
q i (x) = x T Q i x
Q i = (Q i ) T .
• J ⊆ {1, 2, . . . , n} is an index set of the integer constrained variables.
F.2.1
The sections
An LP formatted file contains a number of sections specifying the objective, constraints, variable
bounds, and variable types. The section keywords may be any mix of upper and lower case letters.