# GloptiNets: Scalable Non-Convex Optimization with Certificates

arXiv: https://arxiv.org/abs/2306.14932 · HTML: https://mlsanity.com/paper/2306.14932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Non-parametric Models for Non-negative Functions](https://mlsanity.com/paper/2007.03926/) (2020)
- [Finding Global Minima via Kernel Approximations](https://mlsanity.com/paper/2012.11978/) (2020)
- [PSD Representations for Effective Probability Models](https://mlsanity.com/paper/2106.16116/) (2021)
- [TSSOS: A Moment-SOS hierarchy that exploits term sparsity](https://mlsanity.com/paper/1912.08899/) (2019)
- [Near-optimal estimation of smooth transport maps with kernel sums-of-squares](https://mlsanity.com/paper/2112.01907/) (2021)
- [Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension](https://mlsanity.com/paper/2003.03210/) (2020)
- [Infinite-Dimensional Sums-of-Squares for Optimal Control](https://mlsanity.com/paper/2110.07396/) (2021)
- [Lasserre hierarchy for large scale polynomial optimization in real and complex variables](https://mlsanity.com/paper/1709.04376/) (2017)
- [Exploiting constant trace property in large-scale polynomial optimization](https://mlsanity.com/paper/2012.08873/) (2020)
- [Exploiting Sparsity in Complex Polynomial Optimization](https://mlsanity.com/paper/2103.12444/) (2021)
- [Non-Convex Optimization with Certificates and Fast Rates Through Kernel Sums of Squares](https://mlsanity.com/paper/2204.04970/) (2022)
- [Exponential convergence of sum-of-squares hierarchies for trigonometric polynomials](https://mlsanity.com/paper/2211.04889/) (2022)
- [An effective version of Schm"udgen's Positivstellensatz for the hypercube](https://mlsanity.com/paper/2109.09528/) (2021)

## Abstract (arXiv)

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.