We introduce a novel approach to perform first-order optimization with orthogonal and
unitary constraints. This approach is based on a parametrization stemming from Lie group …

Manifold optimization is ubiquitous in computational and applied mathematics, statistics,
engineering, machine learning, physics, chemistry, etc. One of the main challenges usually …

We consider optimization problems over the Stiefel manifold whose objective function is the
summation of a smooth function and a nonsmooth function. Existing methods for solving this …

We consider the vector embedding problem. We are given a finite set of items, with the goal
of assigning a representative vector to each one, possibly under some constraints (such as …

The ability of multiple-input multiple-output (MIMO) radar systems to adapt waveforms across
antennas allows flexibility in the transmit beampattern design. In cognitive radar, a popular …

Strictly enforcing orthonormality constraints on parameter matrices has been shown
advantageous in deep learning. This amounts to Riemannian optimization on the Stiefel …

We perform quantum process tomography (QPT) for both discrete-and continuous-variable
quantum systems by learning a process representation using Kraus operators. The Kraus …

In this paper we propose a new Riemannian conjugate gradient method for optimization on
the Stiefel manifold. We introduce two novel vector transports associated with the retraction …

Let f be a real-valued function on a Riemannian submanifold of a Euclidean space, and let
̄f be a local extension of f. We show that the Riemannian Hessian of f can be conveniently …

A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and
to allow the stable propagation of signals over long time scales, is to constrain recurrent …