MOSEK does not solve non-convex problems for the following reasons:
- The algorithms employed in MOSEK require convexity and cannot be applied to non-convex problems.
- It is in general impossible to measure the optimality or quality of a solution for a non-convex problem. This fits very badly into the general MOSEK framework.
In many cases a convex approximation of a non-convex problem will behave significantly better in several ways:
- The algorithms applied by MOSEK will (theoretically) always converge toward a global optimum.
- MOSEK will often be able to determine infeasibility or unboundedness of a problem.
- Global optimality of a solution can be proved within small margins.