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

Chapter 6
Nonlinear API tutorial
This chapter provides information about how to solve general convex nonlinear optimization problems
using MOSEK. By general nonlinear problems it is meant problems that cannot be formulated as a
conic quadratic optimization or a convex quadratically constrained optimization problem.
In general it is recommended not to use nonlinear optimizer unless needed. The reasons are
• MOSEK has no way of checking whether the formulated problem is convex and if this assumption
is not satisfied the optimizer will not work.
• The nonlinear optimizer requires 1st and 2nd order derivative information which is hard to provide
correctly i.e. it is nontrivial to program the code that computes the derivative information.
• The specification of nonlinear problems requires C function callbacks. Such C function callbacks
cannot be dump to disk and that makes it hard to report issues to MOSEK support.
• The algorithm employed for nonlinear optimization problems is not as good as the one employed
for conic problems i.e. conic problems has special that can be exploited to make the optimizer
faster and more robust.
This leads to following advices in decreasing order of importance.
• Consider reformulating the problem to a conic quadratic optimization problem if at all possible.
In particular many problems involving polynomial terms can easily be reformulated to conic
quadratic form.
• Consider reformulating the problem to a separable optimization problem because that simplifies
the issue with verifying convexity and computing 1st and 2nd order derivatives significantly. In
most cases problems on separable form also solves faster because of the simpler structure of the
functions. In Section 6.1 some utility code that makes it easy to solve separable problems is
discussed.
• Finally, if the problem cannot be reformulated to separable form then use a modelling language
like AMPL or GAMS. The reason is the modeling language will do all the computing of function
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