# New merit functions for multiobjective optimization and their properties

arXiv: https://arxiv.org/abs/2010.09333 · HTML: https://mlsanity.com/paper/2010.09333/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2020.

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

- [Bilevel Data Curation for LLM Fine-tuning: Offline Selection and Online Self-Refining Generation](https://mlsanity.com/paper/2511.21056/) (2025)
- [A globally convergent fast iterative shrinkage-thresholding algorithm with a new momentum factor for single and multi-objective convex optimization](https://mlsanity.com/paper/2205.05262/) (2022)

## Abstract (arXiv)

A merit (gap) function is a map that returns zero at the solutions of problems and strictly positive values otherwise. Its minimization is equivalent to the original problem by definition, and it can estimate the distance between a given point and the solution set. Ideally, this function should have some properties, including the ease of computation, continuity, differentiability, boundedness of the level set, and error boundedness. In this work, we propose new merit functions for multiobjective optimization with lower semicontinuous objectives, convex objectives, and composite objectives, and we show that they have such desirable properties under reasonable assumptions.