  For multiparametric mixed-integer convex programming problems such as those
encountered in hybrid model predictive control, we propose an algorithm for
generating a feasible partition of a subset of the parameter space. The result
is a static map from the current parameter to a suboptimal integer solution
such that the remaining convex program is feasible. Convergence is proven with
a new insight that the overlap among the feasible parameter sets of each
integer solution governs the partition complexity. The partition is stored as a
tree which makes querying the feasible solution efficient. The algorithm can be
used to warm start a mixed integer solver with a real-time guarantee or to
provide a reference integer solution in several suboptimal MPC schemes. The
algorithm is tested on randomly generated systems with up to six states,
demonstrating the effectiveness of the approach.
