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Efficient methods to provide sub-optimal solutions to non-convex optimizationproblems with knowledge of the solution's sub-optimality would facilitate thewidespread application of nonlinear optimal control algorithms. To that end,leveraging recent work in risk-aware verification, we provide two algorithms to(1) probabilistically bound the optimality gaps of solutions reported by novelpercentile optimization techniques, and (2) probabilistically bound the maximumoptimality gap reported by percentile approaches for repetitive applications,e.g. Model Predictive Control (MPC). Notably, our results work for a largeclass of optimization problems. We showcase the efficacy and repeatability ofour results on a few, benchmark non-convex optimization problems and theutility of our results for controls in a Nonlinear MPC setting.

Bounding Optimality Gaps for Non-Convex Optimization Problems: Applications to Nonlinear Safety-Critical Systems