A variety of hybrids of Constraint Programming, Artificial Intelligence and Operations Research techniques have given impressive results. Three recent approaches are (i) the use of relaxations in constraint systems, (ii) non-systematic backtracking to boost the scalability of constraint solvers, and (iii) non-systematic backtracking to boost the scalability of branch-and-bound search. This paper describes a hybrid of all three approaches that combines non-systematic backtracking, SAT-based inference and linear relaxation. It is intended for large MIPs that are hard for reasons of both optimisation and feasibility. Such problems are of practical as well as theoretical interest and we expect the hybrid to find many applications. It is currently under development and results will be reported at the workshop.