The MOSEK command line tool Version 7.0 (Revision 141)

13.1. MPS FILE STRUCTURE 285
Next define
x 1 =
⎡
⎣ x 1
x 4
x 7
⎤
⎦ and x 2 =
⎡
⎢
⎣
x 6
x 5
x 3
x 2
⎤
⎥
⎦ .
where C t must have one of the following forms
• R set:
C := { x ∈ R n : x t ∈ C t , t = 1, . . . , k }
C t = {x ∈ R nt }.
• Quadratic cone:
⎧
⎨
C t =
⎩ x ∈ ∑
: x Rnt 1 ≥ √ nt
j=2
x 2 j
⎫
⎬
⎭ . (13.2)
• Rotated quadratic cone:
⎧
⎨
C t =
⎩ x ∈ : 2x Rnt 1 x 2 ≥
⎫
∑n t
⎬
x 2 j, x 1 , x 2 ≥ 0
⎭ . (13.3)
j=3
In general, only quadratic and rotated quadratic cones are specified in the MPS file whereas membership
of the R set is not. If a variable is not a member of any other cone then it is assumed to be a member
of an R cone.
Next, let us study an example. Assume that the quadratic cone
and the rotated quadratic cone
x 4 ≥
√
x 2 5 + x2 8 (13.4)
2x 3 x 7 ≥ x 2 1 + x 2 0, x 3 , x 7 ≥ 0, (13.5)
should be specified in the MPS file. One CSECTION is required for each cone and they are specified as
follows:
* 1 2 3 4 5 6
*23456789012345678901234567890123456789012345678901234567890
CSECTION konea 0.0 QUAD
x4
x5
x8