  Since more than three decades, interior-point methods proved very useful for
optimization, from linear over semidefinite to conic (and partly beyond
non-convex) programming; despite the fact that already in the semidefinite case
(even when strong duality holds) "hard" problems are known. We shade a light on
a rather surprising restriction in the non-commutative world (of semidefinite
programming), namely "commutative" paths and propose a new family of solvers
that is able to use the full richness of "non-commutative" search directions:
(primal) feasible-interior-point methods. Beside a detailed basic discussion,
we illustrate some variants of "non-commutative" paths and provide a simple
implementation for further (problem specific) investigations.
