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

A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…

A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…

Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning…

Second-order optimization uses curvature information about the objective function, which can help in faster convergence. However, such methods typically require expensive computation of the Hessian matrix, preventing their usage in a…

To treat the electronic structure of large molecules by electron propagator methods we developed a parallel computer program called P-RICD$\Sigma$. The program exploits the sparsity of the two-electron integral matrix by using Cholesky…

Best rank-one approximation is one of the most fundamental tasks in tensor computation. In order to fully exploit modern multi-core parallel computers, it is necessary to develop decoupling algorithms for computing the best rank-one…

We present the implementation of a quadratically convergent Self-consistent field (QCSCF) algorithm based on an adaptive trust-radius optimization scheme for restricted open-shell Hartree-Fock (ROHF), restricted Hartree-Fock (RHF), and…

We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost…

In this paper, we propose a new set of midpoint-based high-order discretization schemes for computing straight and mixed nonlinear second derivative terms that appear in the compressible Navier-Stokes equations. Firstly, we detail a set of…

In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…

The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose…

Dual decomposition is a powerful technique for deriving decomposition schemes for convex optimization problems with separable structure. Although the Augmented Lagrangian is computationally more stable than the ordinary Lagrangian, the…

We review strategies for differentiating matrix-based computations, and derive symbolic and algorithmic update rules for differentiating expressions containing the Cholesky decomposition. We recommend new `blocked' algorithms, based on…

An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…

In this work we derive a second-order approach to bilevel optimization, a type of mathematical programming in which the solution to a parameterized optimization problem (the "lower" problem) is itself to be optimized (in the "upper"…

Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in \emph{second-order} methods, which rely…

We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…

We propose a new algorithm for efficiently solving the damped Fisher matrix in large-scale scenarios where the number of parameters significantly exceeds the number of available samples. This problem is fundamental for natural gradient…

We consider an inertial primal-dual algorithm to compute the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…

A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…