# A generalized conditional gradient method for multiobjective composite optimization problems

arXiv: https://arxiv.org/abs/2302.12912 · HTML: https://mlsanity.com/paper/2302.12912/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2023.

## Built on by (most cited first, 2 of 2)

- [Common pitfalls to avoid while using multiobjective optimization in machine learning](https://mlsanity.com/paper/2405.01480/) (2024)
- [Adaptive Lipschitz-Free Conditional Gradient Methods for Stochastic Composite Nonconvex Optimization](https://mlsanity.com/paper/2603.06369/) (2026)

## Abstract (arXiv)

This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these problems, we propose a generalized version of the conditional gradient method, also known as Frank-Wolfe method. The method is analyzed with three step size strategies, including Armijo-type, adaptive, and diminishing step sizes. We establish asymptotic convergence properties and iteration-complexity bounds, with and without convexity assumptions on the objective functions. Numerical experiments illustrating the practical behavior of the methods are presented.