# GloptiNets: Scalable Non-Convex Optimization with Certificates Source: [GloptiNets: Scalable Non-Convex Optimization with Certificates]() Collection index: [llms.txt]() Data updated: 2026-01-01T12:38:45.355Z Authors: Gaspard Beugnot, Julien Mairal, Alessandro Rudi Published: 2023-06-26T09:42:59.000Z ## Abstract We present a novel approach to non-convex optimization with certificates, which handles smooth functions on the hypercube or on the torus. Unlike traditional methods that rely on algebraic properties, our algorithm exploits the regularity of the target function intrinsic in the decay of its Fourier spectrum. By defining a tractable family of models, we allow at the same time to obtain precise certificates and to leverage the advanced and powerful computational techniques developed to optimize neural networks. In this way the scalability of our approach is naturally enhanced by parallel computing with GPUs. Our approach, when applied to the case of polynomials of moderate dimensions but with thousands of coefficients, outperforms the state-of-the-art optimization methods with certificates, as the ones based on Lasserre's hierarchy, addressing problems intractable for the competitors. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Global Non-convex Optimization on Random Trigonometric Polynomials](): Global non-convex optimization; Random trigonometric polynomials; Certification Success Rate: 0.0476. - [Global polynomial optimization on Random Chebychev polynomials](): Global polynomial optimization; Random Chebychev polynomials; Certificate Error: 0.0036. ## Original sources and implementation [Original paper]() [PDF]() [Implementation]()