The Riemannian Multiobjective Proximal Gradient Method (RMPGM) directly optimizes vector-valued composite objectives on Riemannian manifolds and converges globally to Pareto stationary points with an O(1/k) rate.
SIAM Journal on Optimization32(4), 2690–2717 (2022)
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Riemannian conditional gradient methods are introduced for composite optimization on manifolds, achieving O(1/k) convergence for adaptive and diminishing steps and O(1/ε²) iteration complexity for Armijo steps.
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A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds
The Riemannian Multiobjective Proximal Gradient Method (RMPGM) directly optimizes vector-valued composite objectives on Riemannian manifolds and converges globally to Pareto stationary points with an O(1/k) rate.
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Riemannian conditional gradient methods for composite optimization problems
Riemannian conditional gradient methods are introduced for composite optimization on manifolds, achieving O(1/k) convergence for adaptive and diminishing steps and O(1/ε²) iteration complexity for Armijo steps.