Related papers: A speed restart scheme for a dynamics with Hessian…
This paper addresses an estimation problem of an additive functional of $\phi$, which is defined as $\theta(P;\phi)=\sum_{i=1}^k\phi(p_i)$, given $n$ i.i.d. random samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet…
The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent…
Large horsepower induction motors play a critical role in the operation of industrial facilities. In this respect, the distribution network operators dedicate a high priority to the operational safety of these motor loads. In this paper,…
Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…
Reformulating hyperdynamics without using a transition state theory (TST) dividing surface makes it possible to accelerate conventional molecular dynamics (MD) simulation using a broader range of bias potentials. A new scheme to calculate…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower…
We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time $O(\epsilon^{-7/4} \log(1/ \epsilon) )$ to find an $\epsilon$-stationary point,…
In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…
By analyzing accelerated proximal gradient methods under a local quadratic growth condition, we show that restarting these algorithms at any frequency gives a globally linearly convergent algorithm. This result was previously known only for…
We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…
Learning rate schedules are ubiquitously used to speed up and improve optimisation. Many different policies have been introduced on an empirical basis, and theoretical analyses have been developed for convex settings. However, in many…
We introduce algorithms for learning nonlinear dynamical systems of the form $x_{t+1}=\sigma(\Theta^{\star}x_t)+\varepsilon_t$, where $\Theta^{\star}$ is a weight matrix, $\sigma$ is a nonlinear link function, and $\varepsilon_t$ is a…
In this work, a nonlinear momentum method is introduced to enhance the convergence performance of momentum-based gradient optimization algorithms. Classical momentum methods, such as the Heavy Ball method, can be viewed as a dynamical…
We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution…
We propose a mathematical formulation of the zeroth law of thermodynamics and develop a stochastic dynamical theory, with a consistent irreversible thermodynamics, for systems possessing sustained conservative stationary current in phase…
I extend the scope of the density matrix renormalization group technique developed by White to the calculation of dynamical correlation functions. As an application and performance evaluation I calculate the spin dynamics of the 1D…
High-index saddle dynamics (HiSD) is an effective approach for computing saddle points of a prescribed Morse index and constructing solution landscapes for complex nonlinear systems. However, for problems with ill-conditioned Hessians…
Accelerated algorithms for minimizing smooth strongly convex functions usually require knowledge of the strong convexity parameter $\mu$. In the case of an unknown $\mu$, current adaptive techniques are based on restart schemes. When the…
This paper develops a new parameter-free restarted method, namely RPF-SFISTA, and a new parameter-free aggressive regularization method, namely A-REG, for solving strongly convex and convex composite optimization problems, respectively.…