Riemannian Preconditioning
Copyright policy )Riemannian Preconditioning
This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian structure is sought on a quotient manifold. The proposed method is shown to be particularly insightful and efficient in quadratic optimization with orthogonality and/or rank constraints, which covers most current applications of Riemannian optimization in matrix manifolds.
- University of Liège Belgium
- University of Cambridge United Kingdom
- Department of Engineering, University of cambridge United Kingdom
generalized eigenvalue problem, Real-valued functions on manifolds, Lyapunov equation, Riemannian optimization, metric tuning, low rank, Methods of successive quadratic programming type, quotient manifold, Numerical mathematical programming methods, Nonlinear programming, Grassmann, Optimization and Control (math.OC), 4903 Numerical and Computational Mathematics, 49 Mathematical Sciences, FOS: Mathematics, Semidefinite programming, Mathematics - Optimization and Control, sequential quadratic programming
generalized eigenvalue problem, Real-valued functions on manifolds, Lyapunov equation, Riemannian optimization, metric tuning, low rank, Methods of successive quadratic programming type, quotient manifold, Numerical mathematical programming methods, Nonlinear programming, Grassmann, Optimization and Control (math.OC), 4903 Numerical and Computational Mathematics, 49 Mathematical Sciences, FOS: Mathematics, Semidefinite programming, Mathematics - Optimization and Control, sequential quadratic programming
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