Related papers: Practical Perspectives on Symplectic Accelerated O…

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…

This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…

With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…

Due to the emergence of symplectic geometry, the geometric treatment of mechanics underwent a great development during the last century. In this scenario the pressence of symmetries in Hamiltonian systems leads naturally to the existence of…

We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…

The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to drastically transform our ability to understand and control complex systems. However, most of…

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…

Gaussian wavepacket dynamics has proven to be a useful semiclassical approximation for quantum simulations of high-dimensional systems with low anharmonicity. Compared to Heller's original local harmonic method, the variational Gaussian…

The combinatorial problem Max-Cut has become a benchmark in the evaluation of local search heuristics for both quantum and classical optimisers. In contrast to local search, which only provides average-case performance guarantees, the…

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…

Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly…

The paper gives a symplectic-geometric account of semiclassical Gaussian wave packet dynamics. We employ geometric techniques to "strip away" the symplectic structure behind the time-dependent Schr\"odinger equation and incorporate it into…

We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral…

Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…