A brief introduction to manifold optimization
Manifold optimization is ubiquitous in computational and applied mathematics, statistics,
engineering, machine learning, physics, chemistry, etc. One of the main challenges usually …
engineering, machine learning, physics, chemistry, etc. One of the main challenges usually …
Efficient spectral computation of the stationary states of rotating Bose–Einstein condensates by preconditioned nonlinear conjugate gradient methods
We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral
spatial discretization scheme for computing the ground states (GS) of rotating Bose–Einstein …
spatial discretization scheme for computing the ground states (GS) of rotating Bose–Einstein …
Adaptive quadratically regularized Newton method for Riemannian optimization
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density
functional theory, Bose--Einstein condensates, low rank nearest correlation, image …
functional theory, Bose--Einstein condensates, low rank nearest correlation, image …
Efficient SAV approach for imaginary time gradient flows with applications to one-and multi-component Bose-Einstein condensates
Efficient and accurate numerical schemes, based on the scalar auxiliary variable (SAV)
approach, are proposed to find the ground state solutions of one-and multi-component Bose …
approach, are proposed to find the ground state solutions of one-and multi-component Bose …
Moment generating function, expectation and variance of ubiquitous distributions with applications in decision sciences: A review
Statistics have been widely used in many disciplines including science, social science,
business, engineering, and many others. One of the most important areas in statistics is to …
business, engineering, and many others. One of the most important areas in statistics is to …
Computation of ground states of the Gross--Pitaevskii functional via Riemannian optimization
In this paper we combine concepts from Riemannian optimization P.-A. Absil, R. Mahony,
and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, Princeton University Press …
and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, Princeton University Press …
Second-order flows for computing the ground states of rotating Bose-Einstein condensates
Second-order flows in this paper refer to some artificial evolutionary differential equations
involving second-order time derivatives distinguished from gradient flows which are …
involving second-order time derivatives distinguished from gradient flows which are …
Constrained high-index saddle dynamics for the solution landscape with equality constraints
We propose a constrained high-index saddle dynamics (CHiSD) method to search for index-
k saddle points of an energy functional subject to equality constraints. With Riemannian …
k saddle points of an energy functional subject to equality constraints. With Riemannian …
Normalized Gradient Flow with Lagrange Multiplier for Computing Ground States of Bose--Einstein Condensates
The normalized gradient flow, ie, the gradient flow with discrete normalization (GFDN)
introduced in [W. Bao and Q. Du, SIAM J. Sci. Comput., 25 (2004), pp. 1674--1697] or the …
introduced in [W. Bao and Q. Du, SIAM J. Sci. Comput., 25 (2004), pp. 1674--1697] or the …
Mathematical models and numerical methods for spinor Bose-Einstein condensates
In this paper, we systematically review mathematical models, theories and numerical
methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) …
methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) …