# Gradient-Based Multiobjective Optimization with Uncertainties

arXiv: https://arxiv.org/abs/1612.03815 · HTML: https://mlsanity.com/paper/1612.03815/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2016.

## Built on by (most cited first, 11 of 11)

- [Independent Component Alignment for Multi-Task Learning](https://mlsanity.com/paper/2305.19000/) (2023)
- [Federated Multi-Objective Learning](https://mlsanity.com/paper/2310.09866/) (2023)
- [Reward-free Alignment for Conflicting Objectives](https://mlsanity.com/paper/2602.02495/) (2026)
- [LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch](https://mlsanity.com/paper/2409.02969/) (2024)
- [Pareto Efficient Fairness in Supervised Learning: From Extraction to Tracing](https://mlsanity.com/paper/2104.01634/) (2021)
- [A Spectral Enabled GAN for Time Series Data Generation](https://mlsanity.com/paper/2103.01904/) (2021)
- [Multi-Objective Optimization for Sparse Deep Multi-Task Learning](https://mlsanity.com/paper/2308.12243/) (2023)
- [A multiobjective continuation method to compute the regularization path of deep neural networks](https://mlsanity.com/paper/2308.12044/) (2023)
- [Federated Communication-Efficient Multi-Objective Optimization](https://mlsanity.com/paper/2410.16398/) (2024)
- [SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion](https://mlsanity.com/paper/2509.21058/) (2025)
- [Adversarial Lagrangian Integrated Contrastive Embedding for Limited Size Datasets](https://mlsanity.com/paper/2210.03261/) (2022)

## Abstract (arXiv)

In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated in a subdivison algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.