相关论文: Higher Order Force Gradient Symplectic Algorithms

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…

This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…

The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…

Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…

The limited memory steepest descent method (Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review this method and propose new variants. For strictly convex…

Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…

Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…

With advances in deep learning, exponential data growth and increasing model complexity, developing efficient optimization methods are attracting much research attention. Several implementations favor the use of Conjugate Gradient (CG) and…

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Variance-reduced gradient estimators for policy gradient methods have been one of the main focus of research in the reinforcement learning in recent years as they allow acceleration of the estimation process. We propose a variance-reduced…

In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…

We show a new simple algorithm that checks whether a given higher-order grammar generates a nonempty language of trees. The algorithm amounts to a procedure that transforms a grammar of order n to a grammar of order n-1, preserving…

We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with…

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…

Policy gradient methods are widely used in reinforcement learning algorithms to search for better policies in the parameterized policy space. They do gradient search in the policy space and are known to converge very slowly. Nesterov…

In this paper, we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian systems. The one class is the symplectic scheme, which contains two new families of…

Many analyses in high-energy physics rely on selection thresholds (cuts) applied to detector, particle, or event properties. Initial cut values can often be guessed from physical intuition, but cut optimization, especially for multiple…

Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy…

Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…