# On Bi-Objective convex-quadratic problems

arXiv: https://arxiv.org/abs/1812.00289 · HTML: https://mlsanity.com/paper/1812.00289/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2018.

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

- [BONO-Bench: A Comprehensive Test Suite for Bi-objective Numerical Optimization with Traceable Pareto Sets](https://mlsanity.com/paper/2601.16970/) (2026)

## Abstract (arXiv)

In this paper we analyze theoretical properties of bi-objective convex-quadratic problems. We give a complete description of their Pareto set and prove the convexity of their Pareto front. We show that the Pareto set is a line segment when both Hessian matrices are proportional. We then propose a novel set of convex-quadratic test problems, describe their theoretical properties and the algorithm abilities required by those test problems. This includes in particular testing the sensitivity with respect to separability, ill-conditioned problems, rotational invariance, and whether the Pareto set is aligned with the coordinate axis.