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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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.
A stateless, SVD-free regularizer approximates polar factors to induce low-rank weight structure during training, enabling better post-training compression of vision models and LLMs at under 8% overhead.
A total-variation robust Plackett-Luce loss whose adversarial ranking is the ascending-score order, with convex offline and weakly-convex online guarantees.
Proves time-averaged reconstruction errors converge to zero in online dynamic inverse problems as noise, algorithmic errors, and regularization vanish with growing horizon.
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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.
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SLORR: Simple and Efficient In-Training Low-Rank Regularization
A stateless, SVD-free regularizer approximates polar factors to induce low-rank weight structure during training, enabling better post-training compression of vision models and LLMs at under 8% overhead.
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Distributionally Robust Listwise Preference Optimization
A total-variation robust Plackett-Luce loss whose adversarial ranking is the ascending-score order, with convex offline and weakly-convex online guarantees.
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Dynamic inverse problems: Online regularisation theory
Proves time-averaged reconstruction errors converge to zero in online dynamic inverse problems as noise, algorithmic errors, and regularization vanish with growing horizon.