This work proposes a new algorithm based on a dissipative relativistic system that normalizes the momentum and may result in more stable/faster optimization, and generalizes both Nesterov and heavy ball.Expand

We generalize our recent construction of the zeros of the Riemann $\zeta$-function to two infinite classes of $L$-functions, Dirichlet $L$-functions and those based on level one modular forms. More… Expand

A generalization of symplectic integrators to non-conservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error, enabling the derivation of ‘rate-matching’ algorithms without the need for a discrete convergence analysis.Expand

This work introduces two new ADMM variants, one based on Nesterov's acceleration and the other inspired by Polyak's heavy ball method, and derives differential inclusions modelling these algorithms in the continuous-time limit.Expand

A full characterization of the convergence of distributed over-relaxed ADMM for the same type of consensus problem in terms of the topology of the underlying graph is provided and a proof of the aforementioned conjecture is shown it is valid for any graph, even the ones whose random walks cannot be accelerated via Markov chain lifting.Expand

We consider the non-trivial zeros of the Riemann $\zeta$-function and two classes of $L$-functions; Dirichlet $L$-functions and those based on level one modular forms. We show that there are an… Expand

We show that there are an infinite number of Riemann zeros on the critical line, enumerated by the positive integers $n=1,2,\dotsc$, whose ordinates can be obtained as the solution of a new… Expand

The aim of this paper is to investigate how various Riemann Hypotheses would follow only from properties of the prime numbers. To this end, we consider two classes of [Formula: see text]-functions,… Expand

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identiﬁcation, we derive… Expand