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Recent road trials have shown that guaranteeing the safety of driving decisions is essential for the wider adoption of autonomous vehicle technology. One promising direction is to pose safety requirements as planning constraints in nonlinear, non-convex optimization problems of motion synthesis. However, many implementations of this approach are limited by uncertain convergence and local optimality of the solutions achieved, affecting overall robustness. To improve upon these issues, we propose a novel two-stage optimization framework: in the first stage, we find a solution to a Mixed-Integer Linear Programming (MILP) formulation of the motion synthesis problem, the output of which initializes a second Nonlinear Programming (NLP) stage. The MILP stage enforces hard constraints of safety and road rule compliance generating a solution in the right subspace, while the NLP stage refines the solution within the safety bounds for feasibility and smoothness. We demonstrate the effectiveness of our framework via simulated experiments of complex urban driving scenarios, outperforming a state-of-the-art baseline in metrics of convergence, comfort and progress.