Related papers: A Caputo fractional derivative-based algorithm for…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
Based on the method of FGD, we apply the method of adaptive gradient descent which uses different step length at different epoch. Adaptive gradient descent performs much better than FGD in the tests and keeps the guarantee of convergence…
We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…
In this paper we derive the fourth-order asymptotic expansions of the trapezoidal approximation for the fractional integral and the $L1$ approximation for the Caputo derivative. We use the expansion of the $L1$ approximation to obtain the…
We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is…
In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…
This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…
This paper proposes a novel Generalized Non-Standard Finite Difference (GNSFD) scheme for the numerical solution of a class of fractional partial differential equations (FrPDEs). The formulation of the method is grounded in optimization and…
This paper introduces Tempered Fractional Gradient Descent (TFGD), a novel optimization framework that synergizes fractional calculus with exponential tempering to enhance gradient-based learning. Traditional gradient descent methods often…
Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
In this paper, we propose a novel machine learning method based on adaptive tensor neural network subspace to solve linear time-fractional diffusion-wave equations and nonlinear time-fractional partial integro-differential equations. In…
This study presents a novel high-order numerical method designed for solving the two-dimensional time-fractional convection-diffusion (TFCD) equation. The Caputo definition is employed to characterize the time-fractional derivative. A weak…
In this paper, we propose a conditional gradient method for solving constrained vector optimization problems with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. When the partial order under…
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…
We describe a family of descent algorithms which generalizes common existing schemes used in applications such as neural network training and more broadly for optimization of smooth functions--potentially for global optimization, or as a…
In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time…
This paper presents a parametric solution to piecewise linear regression through the Adaptive Block Gradient Descent (ABGD) algorithm. The heart of the method is the parametrization of piecewise linear functions as the difference of…
In federated learning (FL), model training performance is strongly impacted by data heterogeneity across clients. Client-drift compensation methods have recently emerged as a solution to this issue, introducing correction terms into local…