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

82 CHAPTER 6. NONLINEAR API TUTORIAL
76
77 oprc = [ mosek.scopr.exp, mosek.scopr.exp ]
78 opric = [ 0, 0 ]
79 oprjc = [ 4, 5 ]
80 oprfc = [ 1.0, 1.0 ]
81 oprgc = [ 1.0, 1.0 ]
82 oprhc = [ 0.0, 0.0 ]
83
84 task.putSCeval(opro, oprjo, oprfo, oprgo, oprho,
85 oprc, opric, oprjc, oprfc, oprgc, oprhc)
86
87 task.optimize()
88
89 res = [ 0.0 ] * numvar
90 task.getsolutionslice(
91 mosek.soltype.itr,
92 mosek.solitem.xx,
93 0, numvar,
94 res)
95
96 print ( "Solution is: %s" % res )
97
98 main()
6.1.3 Ensuring convexity and differentiability
Some simple rules can be set up to ensure that the problem satisfies MOSEK’s convexity and differentiability
requirements. First of all, for any variable x i used in a separable term, the variable bounds
must define a range within which the function is twice differentiable.
We can define these bounds as follows:
Separable function Operator name Safe x bounds
fxln(x) scopr.ent 0 < x.
fe gx+h scopr.exp −∞ < x < ∞.
fln(gx + h) scopr.log If g > 0: −h/g < x.
If g < 0: x < −h/g.
f(x + h) g scopr.pow If g > 0 and integer: −∞ < x < ∞.
If g < 0 and integer: either −h < x or x < −h.
Otherwise: −h < x.
To ensure convexity, we require that each z i (x) is either a sum of convex terms or a sum of concave
terms. The following table lists convexity for the relevant ranges for f > 0 — changing the sign of f
switches concavity/convexity.