  Feasibility pumps are highly effective primal heuristics for mixed-integer
linear and nonlinear optimization. However, despite their success in practice
there are only few works considering their theoretical properties. We show that
feasibility pumps can be seen as alternating direction methods applied to
special reformulations of the original problem, inheriting the convergence
theory of these methods. Moreover, we propose a novel penalty framework that
encompasses this alternating direction method, which allows us to refrain from
random perturbations that are applied in standard versions of feasibility pumps
in case of failure. We present a convergence theory for the new penalty based
alternating direction method and compare the new variant of the feasibility
pump with existing versions in an extensive numerical study for mixed-integer
linear and nonlinear problems.
