  We study infeasible-start primal-dual interior-point methods for convex
optimization problems given in a typically natural form we denote as
Domain-Driven formulation. Our algorithms extend many advantages of primal-dual
interior-point techniques available for conic formulations, such as the current
best complexity bounds, and more robust certificates of approximate optimality,
unboundedness, and infeasibility, to Domain-Driven formulations. The complexity
results are new for the infeasible-start setup used, even in the case of linear
programming. In addition to complexity results, our algorithms aim for
expanding the applications of, and software for interior-point methods to wider
classes of problems beyond optimization over symmetric cones.
