… Our methods are discretizations of conformal Hamiltonian dynamics, which generalize the
classical momentum method … We study in detail one implicit and two explicit methods. For one …

… and so we refer to (2) as Hamiltonian descent equations. Note that this flow is different to the
… Hamiltonian mechanics studied in [12, 13], which are also Hamiltonian descent methods but …

… Hamiltonian-based perspective to generalize Nesterov’s accelerated gradient descent and
Polyak’s heavy ball method … In this paper, we take a Hamiltonian-based perspective to derive …

… a family of quantum gradient descent algorithms that we will refer to as Quantum … methods
via discretizations of conformal Hamiltonian dynamics, known as Hamiltonian descent methods…

… We show that Hamiltonian Descent has a better convergence rate than the Chebyshev method
for … We will soon show that Hamiltonian Descent is a “descent” method; more precisely, it …

… In this work, we focus on the class of stochastic Hamiltonian methods and … Hamiltonian
gradient descent (SHGD), and propose the first stochastic variance reduced Hamiltonian method, …

… the Hamiltonian nullspace shuttle can be interpreted as a hybrid between Monte Carlo samplers
and gradient-based descent methods… a family of gradient descent methods, as shown in …

… Karmarkar's algorithm, an interior point method for linear programming, has received much
attention in the literature over the past few years and has spawned many variants. Recently …

… descent (SGD) with momentum. In this article, we study these types of methods through the
lens of dissipative Hamiltonian … discretizations of dissipative Hamiltonian systems, where the …

… We show the effectiveness of the fast gradient method compared to the other approaches …
Moreover, the algorithms terminates when it cannot find a descent direction (note that we tried …