Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread 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 novel percentile optimization techniques, and (2) probabilistically bound the maximum optimality gap reported by percentile approaches for repetitive applications, e.g. Model Predictive Control (MPC). Notably, our results work for a large class of optimization problems. We showcase the efficacy and repeatability of our results on a few, benchmark non-convex optimization problems and the utility of our results for controls in a Nonlinear MPC setting.

翻译：提供具有次优性认知的非凸优化问题高效求解方法，将极大促进非线性最优控制算法的广泛应用。基于此，我们借鉴近期风险感知验证领域的研究成果，提出两种算法：(1) 对新型百分位优化技术所得解的优化性差距进行概率界定的方法；(2) 针对重复性应用场景（如模型预测控制）中百分位方法报告的最大优化性差距进行概率界定的方法。值得注意的是，本研究成果适用于大规模优化问题。通过在多个基准非凸优化问题上的实验验证了方法的有效性与可重复性，并在非线性模型预测控制框架中展示了本研究成果对控制领域的实用价值。