A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds

Kangming Chen

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arXiv · 2605.16731

A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds

Kangming Chen

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Abstract

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and establishes global convergence to Pareto stationary points, together with an $\mathcal{O}(1/k)$ convergence rate. We further develop two variants to enhance practicality and performance: an inexact RMPGM that allows controlled inexactness in solving subproblems, and a trust-region RMPGM that adaptively adjusts the penalty parameter and achieves an $\mathcal{O}(\epsilon^{-2}) $iteration complexity. Numerical experiments demonstrate that the proposed methods are consistently outperform subgradient-based baselines.

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Kangming Chen. 2026-05-16. A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds. https://arxiv.org/abs/2605.16731

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