相关论文: A Second-Order CASSCF Algorithm with the Cholesky …

In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for…

Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…

Despite the many advances in the use of weakly-compressible smoothed particle hydrodynamics (SPH) for the simulation of incompressible fluid flow, it is still challenging to obtain second-order convergence even for simple periodic domains.…

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…

A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set…

The efficiency of the recently proposed iCIPT2 [iterative configuration interaction (iCI) with selection and second-order perturbation theory (PT2); J. Chem. Theory Comput. 16, 2296 (2020)] for strongly correlated electrons is further…

The difference-of-convex (DC) program is an important model in nonconvex optimization due to its structure, which encompasses a wide range of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where…

In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage…

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…

We investigate the problem of sequential linear data prediction for real life big data applications. The second order algorithms, i.e., Newton-Raphson Methods, asymptotically achieve the performance of the "best" possible linear data…

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific…

In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining feasibility of the iterates is based on a "retraction" idea…

Finding robot poses and trajectories represents a foundational aspect of robot motion planning. Despite decades of research, efficiently and robustly addressing these challenges is still difficult. Existing approaches are often plagued by…

This paper is concerned with finding an optimal algorithm for minimizing a composite convex objective function. The basic setting is that the objective is the sum of two convex functions: the first function is smooth with up to the d-th…

This paper proposes algorithms for learning two-level Boolean rules in Conjunctive Normal Form (CNF, i.e. AND-of-ORs) or Disjunctive Normal Form (DNF, i.e. OR-of-ANDs) as a type of human-interpretable classification model, aiming for a…

We present an efficient orbital optimization procedure that combines the highly GPU accelerated, spin-adapted density matrix renormalization group (DMRG) method with the complete active space self-consistent field (CAS-SCF) approach for…

Second-order optimizers are thought to hold the potential to speed up neural network training, but due to the enormous size of the curvature matrix, they typically require approximations to be computationally tractable. The most successful…

Trust region and cubic regularization methods have demonstrated good performance in small scale non-convex optimization, showing the ability to escape from saddle points. Each iteration of these methods involves computation of gradient,…

Polar codes are a class of channel capacity achieving codes that has been selected for the next generation of wireless communication standards. Successive-cancellation (SC) is the first proposed decoding algorithm, suffering from mediocre…

We study adaptive (or online) nonlinear regression with Long-Short-Term-Memory (LSTM) based networks, i.e., LSTM-based adaptive learning. In this context, we introduce an efficient Extended Kalman filter (EKF) based second-order training…