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February 7, 2026Mathematical Programming

A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints

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Authors

BGBin GaoBGBin GaoYYYa-xiang Yuan

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Overview

This framework improves optimization using tangent cone decoupling and applies to deep learning and model reduction.

Key Points

  • The research aims to develop a space-decoupling framework for optimization involving bounded-rank matrices with constraints.
  • Proposed a new framework for low-rank optimization involving orthogonally invariant constraints.
  • Utilized tangent cones of constraints to simplify the optimization problem.
  • Implemented Riemannian algorithms on the derived smooth manifold.
  • Demonstrated the equivalence of the reformulated and original optimization problems.
  • Showed improvements through numerical experiments in various applications like deep learning and model reduction.

Cite This Study

Gao et al. (2026) studied this question.

synapsesocial.com/papers/698692e89d267392364c9a28https://doi.org/10.1007/s10107-026-02331-7
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