# Parametric Nonconvex Optimization via Convex Surrogates

arXiv: https://arxiv.org/abs/2604.05640 · HTML: https://mlsanity.com/paper/2604.05640/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Clarabel: An interior-point solver for conic programs with quadratic objectives](https://mlsanity.com/paper/2405.12762/) (2024)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [Automatically Learning Compact Quality-aware Surrogates for Optimization Problems](https://mlsanity.com/paper/2006.10815/) (2020)
- [Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers](https://mlsanity.com/paper/2508.10480/) (2025)
- [An L-BFGS-B approach for linear and nonlinear system identification under ℓ1 and group-Lasso regularization](https://mlsanity.com/paper/2403.03827/) (2024)
- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)
- [Learning Parametric Convex Functions](https://mlsanity.com/paper/2506.04183/) (2025)
- [Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates](https://mlsanity.com/paper/2602.18331/) (2026)
- [Latent Linear Quadratic Regulator for Robotic Control Tasks](https://mlsanity.com/paper/2407.11107/) (2024)

## Built on by (most cited first, 1 of 1)

- [SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions](https://mlsanity.com/paper/2604.22355/) (2026)

## Abstract (arXiv)

This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions, given by the composition of convex and monotonic terms, so that the surrogate problem can be solved directly through parallel convex optimization. As a proof of concept, numerical experiments on a nonconvex path tracking problem confirm the approximation quality of the proposed method.