相关论文: Hybrid-Cubic-Rational Semi-Lagrangian Method with …

We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…

In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…

The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

Many popular methods for the calculation of chemical potentials rely on the insertion of test particles into the target system. In the case of liquids and liquid mixtures, this procedure increases in difficulty upon increasing density or…

This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal…

Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…

We present a new discretization for advection-diffusion problems with Robin boundary conditions on complex time-dependent domains. The method is based on second order cut cell finite volume methods introduced by Bochkov et al. to discretize…

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation…

The fundamental purpose of the present work is to constitute an enhanced Euler method with adaptive inverse-quadratic and inverse-multi-quadratic radial basis function (RBF) interpolation technique to solve initial value problems. These…

We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for…

Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…

A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…

We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…

We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit…

In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection…

In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…

The semi-relativistic equation is cast into a second-order Schrodinger-like equation with the inclusion of relativistic corrections up to order (v/c)^2. The resulting equation is solved via the shifted-l expansion technique, which has been…

We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the $p$-norm function, where $p$…

Various algebraic structures of degenerate four-wave mixing equations of optical phase conjugation are analyzed. Two approaches (the spinorial and the Lax-pair based), complementary to each other, are utilized for a systematic derivation of…