Related papers: Derivative-free discrete gradient methods

In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.

The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing…

This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…

In this paper we consider bound-constrained mixed-integer optimization problems where the objective function is differentiable w.r.t.\ the continuous variables for every configuration of the integer variables. We mainly suggest to exploit…

Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…

A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms…

An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…

In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…

This paper applies the gradient discretisation method (GDM) for fourth order elliptic variational inequalities. The GDM provides a new formulation of error estimates and a complete convergence analysis of several numerical methods. We show…

A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is…

Stochastic optimization problems with unknown decision-dependent distributions have attracted increasing attention in recent years due to its importance in applications. Since the gradient of the objective function is inaccessible as a…

Derivative-free optimization algorithms are particularly useful for tackling blackbox optimization problems where the objective function arises from complex and expensive procedures that preclude the use of classical gradient-based methods.…

Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but…

Zeroth-order optimization methods are developed to overcome the practical hurdle of having knowledge of explicit derivatives. Instead, these schemes work with merely access to noisy functions evaluations. One of the predominant approaches…

The discrete gradient approach is generalized to yield integral preserving methods for differential equations in Lie groups.

In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…

In this paper we analyze the necessary number of samples to estimate the gradient of any multidimensional smooth (possibly non-convex) function in a zero-order stochastic oracle model. In this model, an estimator has access to noisy values…

Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in…

Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…