# A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems

arXiv: https://arxiv.org/abs/1712.03005 · HTML: https://mlsanity.com/paper/1712.03005/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2017.

## Built on by (most cited first, 5 of 5)

- [Pareto Set Learning for Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2501.06773/) (2025)
- [PMGDA: A Preference-based Multiple Gradient Descent Algorithm](https://mlsanity.com/paper/2402.09492/) (2024)
- [FERERO: A Flexible Framework for Preference-Guided Multi-Objective Learning](https://mlsanity.com/paper/2412.01773/) (2024)
- [Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art](https://mlsanity.com/paper/2412.01566/) (2024)
- [A Tale of Two Problems: Multi-Task Bilevel Learning Meets Equality Constrained Multi-Objective Optimization](https://mlsanity.com/paper/2605.09094/) (2026)

## Abstract (arXiv)

In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.