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

78 CHAPTER 6. NONLINEAR API TUTORIAL
values and derivatives. This eliminates an important source of errors. Therefore, it is strongly
recommended to use a modelling language at the protype stage.
6.1 Separable convex (SCopt) interface
The MOSEK Python API provides a way to add simple non-linear functions composed from a limited
set of non-linear terms. Non-linear terms can be mixed with quadratic terms in objective and
constraints.
We consider a normal linear problem with additional non-linear terms z:
minimize
z 0 (x) + c T x
subject to li c ≤ z i (x) + a T i x ≤ u c i, i = 1 . . . m
l x ≤ x ≤ u x ,
x ∈ R n
z : R n → R (m+1)
Using the separable non-linear interface it is possible to add non-linear functions of the form
∑K i
z i (x) = wk(x i pik ), wk i : R → R
k=1
In other words, each non-linear function z i is a sum of separable functions wk i of one variable each. A
limited set of functions are supported; each wk i can be one of the separable functions:
where f, g and h are constants.
Separable function Operator name
fxln(x) scopr.ent Entropy function
fe gx+h scopr.exp Exponential function
fln(gx + h) scopr.log Logarithm
f(x + h) g scopr.pow Power function
This formulation does not guarantee convexity. For MOSEK to be able to solve the problem, following
requirements must be met:
• If the objective is minimized, the sum of non-linear terms must be convex, otherwise it must be
concave.
• Any constraint bounded below must be concave, and any constraint bounded above must be
convex.
• Each separable term must be twice differentiable within the bounds of the variable it is applied
to.
If these are not satisfied MOSEK may not be able to solve the problem or produce a meaningful status
report. For details see section 6.1.3.