Related papers: Arbitrary-order functionally fitted energy-diminis…
This paper addresses the numerical solution of nonlinear eigenvector problems such as the Gross-Pitaevskii and Kohn-Sham equation arising in computational physics and chemistry. These problems characterize critical points of energy…
Derivative-free Riemannian optimization (DFRO) aims to minimize an objective function using only function evaluations, under the constraint that the decision variables lie on a Riemannian manifold. The rapid increase in problem dimensions…
We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly…
The gradient expansion of the kinetic energy functional, when applied for atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the…
In this paper, we extend a recently established subgradient method for the computation of Riemannian metrics that optimizes certain singular value functions associated with dynamical systems. This extension is threefold. First, we introduce…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
We study a problem of damping a control system described by functional-differential equations of natural order $n$ and neutral type with non-smooth complex coefficients on an arbitrary tree with global delay. The latter means that the delay…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
In this paper, we develop a novel class of arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation. With the aid of the invariant energy quadratization approach, the Camassa-Holm equation is first reformulated into an…
Anderson acceleration (AA) as an efficient technique for speeding up the convergence of fixed-point iterations may be designed for accelerating an optimization method. We propose a novel optimization algorithm by adapting Anderson…
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…
In this paper, we propose Riemannian conditional gradient methods for minimizing composite functions, i.e., those that can be expressed as the sum of a smooth function and a retraction-based convex function. We analyze the convergence of…
We introduce a robust optimization method for flip-free distortion energies used, for example, in parametrization, deformation, and volume correspondence. This method can minimize a variety of distortion energies, such as the symmetric…
This paper presents a novel Riemannian conjugate gradient method for the Kohn-Sham energy minimization problem in density functional theory (DFT), with a focus on non-metallic crystal systems. We introduce an energy-adaptive metric that…
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…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
We present a high order scheme for approximating kinetic equations with stiff relaxation. The objective is to provide efficient methods for solving the underlying system of conservation laws. The construction is based on several…
Vibrating systems can respond to an infinite number of initial conditions and the overall dynamics of the system can be strongly affected by them. Therefore, it is of practical importance to have methods by which we can determine the…
We present a second-order strictly length-preserving and unconditionally energy-stable rotational discrete gradient (Rdg) scheme for the numerical approximation of the Oseen-Frank gradient flows with anisotropic elastic energy functional.…
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…