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.
Classics in Applied Mathe- matics, vol
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Nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity, applied to quasi-optimal finite-element error estimates for viscous Hamilton-Jacobi equations and second-order mean field games.
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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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A nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity techniques and applications to nonlinear PDEs
Nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity, applied to quasi-optimal finite-element error estimates for viscous Hamilton-Jacobi equations and second-order mean field games.