This NSF CAREER project aims to make autonomous systems safer and more reliable by developing optimization tools that are both fast and theoretically sound. Many high-stakes autonomy tasks—building 3D maps from images, planning robot motions, or choosing actions from raw sensor data—are formulated as nonconvex optimization problems that today are typically handled by heuristics that can fail unpredictably. This project will bring transformative change by enabling “certifiable” decision-making: algorithms that return high-performance solutions together with mathematical certificates of global (or near-global) optimality, so practitioners can verify when an answer is trustworthy. This will be achieved by creating a unified open-source toolbox for fast, certifiable perception, and control and validating it on real robotic platforms and public benchmarks. The intellectual merit of the project includes new theory and algorithms that bridge nonconvex autonomy problems with scalable convex relaxations, and methods that tightly integrate optimization with modern learning systems. The broader impacts of the project include open educational resources and software that democratize trustworthy autonomy, integration into undergraduate and graduate courses, and hands-on mentoring and outreach opportunities that prepare students—from high school to graduate levels—for careers at the intersection of optimization, robotics, and AI. Technically, this project will advance the moment and sums