发表机构
Southwest University; ICTEAM Institute, UCLouvain（西南大学; UCLouvain ICTEAM研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于Hermite插值的黎曼流形双目标优化帕累托前沿逼近方法，无需多初始点即可生成连续前沿，具有收敛性保证和高精度，并成功应用于稀疏主成分分析。
AI 中文摘要
我们提出了一种基于Hermite插值技术的帕累托前沿逼近（MPFA）方法，用于解决黎曼流形上的光滑双目标优化问题。与现有的多目标优化数值算法相比，所提方法无需多个初始点即可生成连续的近似帕累托前沿。我们建立了该方法的收敛性，并分析了所得帕累托前沿的逼近误差。在多个测试问题上的数值实验表明，所提方法能够以高精度和合理的计算成本有效逼近帕累托前沿。此外，该方法被应用于稀疏主成分分析的双目标表述，展示了其在数据分析问题中的实际适用性。
英文摘要
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.
