Melvin Leok

Publication Activity (10 Years)

Years Active: 2005-2024
Publications (10 Years): 37

Top Topics

Variational Formulation

Geometric Methods

Top Venues

J. Nonlinear Sci.

Found. Comput. Math.

SIAM J. Matrix Anal. Appl.

Publications

Brian K. Tran, Ben S. Southworth, Melvin Leok
On Properties of Adjoint Systems for Evolutionary PDEs. CoRR (2024)
Brian K. Tran, Melvin Leok
Geometric Methods for Adjoint Systems. J. Nonlinear Sci. 34 (1) (2024)
Wu Lin, Valentin Duruisseaux, Melvin Leok, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt
Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning. ICML (2023)
Brian K. Tran, Melvin Leok
Type II Hamiltonian Lie Group Variational Integrators with Applications to Geometric Adjoint Sensitivity Analysis. CoRR (2023)
Wu Lin, Valentin Duruisseaux, Melvin Leok, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt
Simplifying Momentum-based Riemannian Submanifold Optimization. CoRR (2023)
Valentin Duruisseaux, Thai P. Duong, Melvin Leok, Nikolay Atanasov
Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems. L4DC (2023)
Kehan Long, Khoa Tran, Melvin Leok, Nikolay Atanasov
Safe Stabilizing Control for Polygonal Robots in Dynamic Elliptical Environments. CoRR (2023)
Valentin Duruisseaux, Melvin Leok
Practical perspectives on symplectic accelerated optimization. Optim. Methods Softw. 38 (6) (2023)
Khoa Tran, Melvin Leok
Lie Group Variational Collision Integrators for a Class of Hybrid Systems. CoRR (2023)
Xuefeng Shen, Khoa Tran, Melvin Leok
High-order symplectic Lie group methods on SO(n) using the polar decomposition. CoRR (2022)
Brian Tran, Melvin Leok
Geometric Methods for Adjoint Systems. CoRR (2022)
Kehan Long, Vikas Dhiman, Melvin Leok, Jorge Cortés, Nikolay Atanasov
Safe Control Synthesis with Uncertain Dynamics and Constraints. CoRR (2022)
Kehan Long, Vikas Dhiman, Melvin Leok, Jorge Cortés, Nikolay Atanasov
Safe Control Synthesis With Uncertain Dynamics and Constraints. IEEE Robotics Autom. Lett. 7 (3) (2022)
Valentin Duruisseaux, Melvin Leok
Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators. J. Nonlinear Sci. 32 (4) (2022)
Álvaro Rodríguez Abella, Melvin Leok
Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups. CoRR (2022)
Valentin Duruisseaux, Thai P. Duong, Melvin Leok, Nikolay Atanasov
Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems. CoRR (2022)
Valentin Duruisseaux, Melvin Leok
A Variational Formulation of Accelerated Optimization on Riemannian Manifolds. SIAM J. Math. Data Sci. 4 (2) (2022)
Brian Tran, Melvin Leok
Multisymplectic Hamiltonian variational integrators. Int. J. Comput. Math. 99 (1) (2022)
Brian Tran, Melvin Leok
Variational Structures in Cochain Projection Based Variational Discretizations of Lagrangian PDEs. CoRR (2021)
Valentin Duruisseaux, Jeremy Schmitt, Melvin Leok
Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization. SIAM J. Sci. Comput. 43 (4) (2021)
Brian Tran, Melvin Leok
Multisymplectic Hamiltonian Variational Integrators. CoRR (2021)
Valentin Duruisseaux, Melvin Leok
Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators. CoRR (2021)
Taeyoung Lee, Molei Tao, Melvin Leok
Variational Symplectic Accelerated Optimization on Lie Groups. CDC (2021)
Melvin Leok
Variational Discretizations of Gauge Field Theories Using Group-Equivariant Interpolation. Found. Comput. Math. 19 (5) (2019)
Xuefeng Shen, Melvin Leok
Geometric exponential integrators. J. Comput. Phys. 382 (2019)
Evan S. Gawlik, Melvin Leok
Embedding-Based Interpolation on the Special Orthogonal Group. SIAM J. Sci. Comput. 40 (2) (2018)
Evan S. Gawlik, Melvin Leok
Interpolation on Symmetric Spaces Via the Generalized Polar Decomposition. Found. Comput. Math. 18 (3) (2018)
Evan S. Gawlik, Melvin Leok
High-Order Retractions on Matrix Manifolds Using Projected Polynomials. SIAM J. Matrix Anal. Appl. 39 (2) (2018)
Yiqun Li, Boying Wu, Melvin Leok
Spectral-collocation variational integrators. J. Comput. Phys. 332 (2017)
James Hall, Melvin Leok
Lie Group Spectral Variational Integrators. Found. Comput. Math. 17 (1) (2017)
Melvin Leok, Jun Zhang
Connecting Information Geometry and Geometric Mechanics. Entropy 19 (10) (2017)
Evan S. Gawlik, Melvin Leok
Iterative Computation of the Fréchet Derivative of the Polar Decomposition. SIAM J. Matrix Anal. Appl. 38 (4) (2017)
Helen Parks, Melvin Leok
Variational Integrators for Interconnected Lagrange-Dirac Systems. J. Nonlinear Sci. 27 (5) (2017)
Yiqun Li, Boying Wu, Melvin Leok
Spectral variational integrators for semi-discrete Hamiltonian wave equations. J. Comput. Appl. Math. 325 (2017)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Global formulations of Lagrangian and Hamiltonian mechanics on two-spheres. CDC (2015)
James Hall, Melvin Leok
Spectral variational integrators. Numerische Mathematik 130 (4) (2015)
Zahra Ebrahimzadeh, Melvin Leok, Mojtaba Mahzoon
A novel variational formulation for thermoelastic problems. Commun. Nonlinear Sci. Numer. Simul. 22 (Issues) (2015)
Joris Vankerschaver, Melvin Leok
A Novel Formulation of Point Vortex Dynamics on the Sphere: Geometrical and Numerical Aspects. J. Nonlinear Sci. 24 (1) (2014)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Dynamics and control of a chain pendulum on a cart. CDC (2012)
Dmitry V. Zenkov, Melvin Leok, Anthony M. Bloch
Hamel's formalism and variational integrators on a sphere. CDC (2012)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Nonlinear robust tracking control of a quadrotor UAV on SE(3). ACC (2012)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3) CoRR (2011)
Nalin A. Chaturvedi, Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Nonlinear Dynamics of the 3D Pendulum. J. Nonlinear Sci. 21 (1) (2011)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Geometric numerical integration for complex dynamics of tethered spacecraft. ACC (2011)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
and SO(3). CDC/ECC (2011)
Melvin Leok, Tomoki Ohsawa
Variational and Geometric Structures of Discrete Dirac Mechanics. Found. Comput. Math. 11 (5) (2011)
Tomoki Ohsawa, Anthony M. Bloch, Melvin Leok
Discrete Hamilton-Jacobi Theory. SIAM J. Control. Optim. 49 (4) (2011)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Geometric tracking control of a quadrotor UAV on SE(3). CDC (2010)
Joris Vankerschaver, Hiroaki Yoshimura, Melvin Leok, Jerrold E. Marsden
Stokes-Dirac structures through reduction of infinite-dimensional Dirac structures. CDC (2010)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Control of Complex Maneuvers for a Quadrotor UAV using Geometric Methods on SE(3). CoRR (2010)
Tomoki Ohsawa, Anthony M. Bloch, Melvin Leok
Discrete Hamilton-Jacobi theory and discrete optimal control. CDC (2010)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Computational geometric optimal control of connected rigid bodies in a perfect fluid. ACC (2010)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Dynamics of connected rigid bodies in a perfect fluid. ACC (2009)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Dynamics of a 3D elastic string pendulum. CDC (2009)
Tomoki Ohsawa, Anthony M. Bloch, Melvin Leok
Discrete Hamilton-Jacobi Theory. CoRR (2009)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Computational Geometric Optimal Control of Rigid Bodies. Commun. Inf. Syst. 8 (4) (2008)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Time optimal attitude control for a rigid body. ACC (2008)
Amit K. Sanyal, Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Global optimal attitude estimation using uncertainty ellipsoids. Syst. Control. Lett. 57 (3) (2008)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Global symplectic uncertainty propagation on SO(3). CDC (2008)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch, Amit K. Sanyal
Global Attitude Estimation using Single Direction Measurements. ACC (2007)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
A combinatorial optimal control problem for spacecraft formation reconfiguration. CDC (2007)
Taeyoung Lee, Nalin A. Chaturvedi, Amit K. Sanyal, Melvin Leok, N. Harris McClamroch
Propagation of uncertainty in rigid body attitude flows. CDC (2007)
Taeyoung Lee, N. Harris McClamroch, Melvin Leok
Optimal Attitude Control for a Rigid Body with Symmetry. ACC (2007)
Islam I. Hussein, Melvin Leok, Amit K. Sanyal, Anthony M. Bloch
A Discrete Variational Integrator for Optimal Control Problems on SO(3). CDC (2006)
Anthony M. Bloch, Melvin Leok, Jerrold E. Marsden, Dmitry V. Zenkov
Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems. CDC (2006)
Taeyoung Lee, N. Harris McClamroch, Melvin Leok
Attitude maneuvers of a rigid spacecraft in a circular orbit. ACC (2006)
Taeyoung Lee, N. Harris McClamroch, Melvin Leok
Optimal Control of a Rigid Body using Geometrically Exact Computations on SE(3). CDC (2006)
Taeyoung Lee, Amit K. Sanyal, Melvin Leok, N. Harris McClamroch
Deterministic Global Attitude Estimation. CDC (2006)
Anthony M. Bloch, Melvin Leok, Jerrold E. Marsden, Dmitry V. Zenkov
Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System. CDC/ECC (2005)