13.8 Supported domains¶
This section lists the domains supported by MOSEK.
13.8.1 Linear domains¶
Each linear domain is determined by the dimension
"zero"
: the zero domain, consisting of the origin ."nonnegative"
: the nonnegative orthant domain ."nonpositive"
: the nonpositive orthant domain ."unbounded"
: the free domain, consisting of the whole .
Membership in a linear domain is equivalent to imposing the corresponding set of
13.8.2 Quadratic cone domains¶
The quadratic domains are determined by the dimension
13.8.3 Exponential cone domains¶
13.8.4 Power cone domains¶
A power cone domain is determined by the dimension
"pow"
: the primal power cone domain is the subset of defined as
where
are the weights normalized to add up to , ie. for . The name reads as “n left”, the length of the product on the left-hand side of the definition.
"dpow"
: the dual power cone domain is the subset of defined as
where
are the weights normalized to add up to , ie. for . The name reads as “n left”, the length of the product on the left-hand side of the definition.
Remark: in MOSEK 9 power cones were available only in the special case with
and weights for some specified as cone parameter.
13.8.5 Geometric mean cone domains¶
A geometric mean cone domain is determined by the dimension
"geomean"
: the primal geometric mean cone domain is the subset of defined as
It is a special case of the primal power cone domain with
and weights .
"dgeomean"
: the dual geometric mean cone domain is the subset of defined as
It is a special case of the dual power cone domain with
and weights .