106 citations · 677 across the 72 of their papers we have counts for
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Practical Perspectives on Symplectic Accelerated Optimization
Valentin Duruisseaux, Melvin Leok
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the v…
Geometric Methods for Adjoint Systems
Brian Tran, Melvin Leok
Adjoint systems are widely used to inform control, optimization, and design in systems described by ordinary differential equations or differential-algebraic equations. In this pap…
Accelerated Optimization on Riemannian Manifolds via Projected Variational Integrators
Valentin Duruisseaux, Melvin Leok
A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian…
Time-adaptive Lagrangian Variational Integrators for Accelerated Optimization on Manifolds
Valentin Duruisseaux, Melvin Leok
A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) and Duruisseaux and Leok (20…
Variational Symplectic Accelerated Optimization on Lie Groups
Taeyoung Lee, Molei Tao, Melvin Leok
There has been significant interest in generalizations of the Nesterov accelerated gradient descent algorithm due to its improved performance guarantee compared to the standard gra…
A Variational Formulation of Accelerated Optimization on Riemannian Manifolds
Valentin Duruisseaux, Melvin Leok
It was shown recently by Su et al. (2016) that Nesterov's accelerated gradient method for minimizing a smooth convex function can be thought of as the time discretization of a…