  We study the projection onto the set of feasible inputs and the set of
feasible solutions of a polynomial optimisation problem (POP). Our motivation
is increasing the robustness of solvers for POP: Without a priori guarantees of
feasibility of a particular instance, one should like to perform the projection
onto the set of feasible inputs prior to running a solver. Without a
certificate of optimality, one should like to project the output of the solver
onto the set of feasible solutions subsequently. We study the computational
complexity, formulations, and convexifications of the projections. Our results
are illustrated on IEEE test cases of Alternating Current Optimal Power Flow
(ACOPF) problem.
