Over the past decade, methods for predicting three-dimensional (3-D) chromosome and
genome structures have proliferated. This has been primarily due to the development of high …

Federated learning (FL) is a promising technique for resolving the rising privacy and security
concerns. Its main ingredient is to cooperatively learn the model among the distributed …

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus
is on problems where the smooth geometry of the search space can be leveraged to design …

This paper develops and analyzes a generalization of the Broyden class of quasi-Newton
methods to the problem of minimizing a smooth objective function f on a Riemannian …

We study the minimization of a convex function f (X) over the set of n\times n positive semi-
definite matrices, but when the problem is recast as\min_U g (U):= f (UU^⊤), with …

This paper explores the well-known identification of the manifold of rank p positive-
semidefinite matrices of size n with the quotient of the set of full-rank n-by-p matrices by the …

Solving the inverse kinematics problem is a fundamental challenge in motion planning,
control, and calibration for articulated robots. Kinematic models for these robots are typically …

We address the numerical problem of recovering large matrices of low rank when most of
the entries are unknown. We exploit the geometry of the low-rank constraint to recast the …

The paper addresses the problem of low-rank trace norm minimization. We propose an
algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed …

Motivated by the problem of learning a linear regression model whose parameter is a large
fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function …