Proposal: Adding Differentiable Multi-Objective Optimization (MOO) Test Functions

Hello,

I'm exploring the possibility of contributing a collection of differentiable multi-objective optimization (MOO) test functions to the `OptimizationProblems.jl` repository. I have personally implemented these functions and their gradients in Julia.

#### Motivation
My main motivation is to use these problems as a standardized testbed for experiments with multi-objective algorithms I'm currently developing. This suite of functions has already been used in several published works, such as:

1. Lucambio Pérez, L. R., & Prudente, L. F. (2018). Nonlinear conjugate gradient methods for vector optimization. SIAM Journal on Optimization, 28(3), 2690-2720.

2. Gonçalves, M. L. N., & Prudente, L. F. (2020). On the extension of the Hager–Zhang conjugate gradient method for vector optimization. Computational Optimization and Applications, 76(3), 889-916.

3. Assunção, P. B., Ferreira, O. P., & Prudente, L. F. (2021). Conditional gradient method for multiobjective optimization. Computational Optimization and Applications, 78(3), 741-768.

4. Gonçalves, M. L. N., Lima, F. S., & Prudente, L. F. (2022). A study of Liu-Storey conjugate gradient methods for vector optimization. Applied Mathematics and Computation, 425, 127099.

5. Gonçalves, M. L. N., Lima, F. S., & Prudente, L. F. (2022). Globally convergent Newton-type methods for multiobjective optimization. Computational Optimization and Applications, 83(2), 403-434.

6. Bello-Cruz, Y., Melo, J. G., Prudente, L. F., & Serra, R. V. G. (2024). A Proximal Gradient Method with an Explicit Line search for Multiobjective Optimization. arXiv preprint arXiv:2404.10993.

7. Lapucci, M., & Mansueto, P. (2023). A limited memory Quasi-Newton approach for multi-objective optimization. Computational Optimization and Applications, 85(1), 33-73.

8. Yang, Y. X., Deng, X., & Tang, L. P. (2025). Global Convergence of a Modified BFGS-Type Method Based on Function Information for Nonconvex Multiobjective Optimization Problems. Journal of the Operations Research Society of China.

9. Chen, W., Tang, L., & Yang, X. (2025). Improvements to steepest descent method for multi-objective optimization. Numerical Algorithms.

10. He, Q. R., Li, S. J., Zhang, B. Y., et al. (2024). A family of conjugate gradient methods with guaranteed positiveness and descent for vector optimization. Computational Optimization and Applications, 89(3), 805-842.

11. Prudente, L. F., & Souza, D. R. (2022). A Quasi-Newton Method with Wolfe Line Searches for Multiobjective Optimization. Journal of Optimization Theory and Applications, 194(3), 1107-1140.

12. Prudente, L. F., & Souza, D. R. (2024). Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems. Computational Optimization and Applications, 88(3), 719-757.

I believe these functions could be useful for researchers working on multi-objective algorithms in Julia and would complement the existing scalar test problems available in the repository.

#### Open Questions
Before proceeding with a more detailed proposal or implementation, I'd like to ask:

1. Would a contribution like this align with the goals of the repository?
2. Would it be acceptable to introduce a new category or model structure for multi-objective problems?
3. Is there any existing effort or recommendation I should be aware of before structuring the code?

#### Additional Information
I'd be happy to follow the design patterns of `OptimizationProblems.jl`, and I'm open to feedback on how best to integrate this kind of functionality.

Looking forward to your thoughts!

Best regards,
**Danilo R. Souza**