MPFA: A Pareto Front Approximation Method for Riemannian Bi-objective Optimization

Abstract

We propose a Pareto front approximation (MPFA) method for smooth bi-objective optimization problems on Riemannian manifolds based on a Hermite interpolation technique. Compared with the existing multiobjective optimization numerical algorithms, the proposed method can generate a continuous approximate Pareto front without multiple initial points. We establish convergence of the proposed method and analyze the approximation error of the resulting Pareto front. Numerical experiments on several test problems demonstrate that the proposed approach can effectively approximate the Pareto front with high accuracy and reasonable computational cost. Furthermore, the method is applied to a bi-objective formulation of sparse principal component analysis, illustrating its practical applicability in data analysis problems.

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BibTeX

@misc{liu2026mpfa,
  title = {{MPFA: A Pareto Front Approximation Method for Riemannian Bi-objective Optimization}},
  author = {Kaiping Liu and P. -A. Absil and Jiawei Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09857},
  eprint = {2609.09857},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09857},
}

RIS

TY  - UNPB
TI  - MPFA: A Pareto Front Approximation Method for Riemannian Bi-objective Optimization
AU  - Kaiping Liu
AU  - P. -A. Absil
AU  - Jiawei Chen
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09857
UR  - https://arxiv.org/abs/2609.09857
AB  - We propose a Pareto front approximation (MPFA) method for smooth bi-objective optimization problems on Riemannian manifolds based on a Hermite interpolation technique. Compared with the existing multiobjective optimization numerical algorithms, the proposed method can generate a continuous approximate Pareto front without multiple initial points. We establish convergence of the proposed method and analyze the approximation error of the resulting Pareto front. Numerical experiments on several test problems demonstrate that the proposed approach can effectively approximate the Pareto front with high accuracy and reasonable computational cost. Furthermore, the method is applied to a bi-objective formulation of sparse principal component analysis, illustrating its practical applicability in data analysis problems.
ER  -

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