相关论文: A generalized formulation for gradient schemes in …

Many supervised learning tasks have intrinsic symmetries, such as translational and rotational symmetry in image classifications. These symmetries can be exploited to enhance performance. We formulate the symmetry constraints into a concise…

In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…

It is well-known that the reparameterisation gradient estimator, which exhibits low variance in practice, is biased for non-differentiable models. This may compromise correctness of gradient-based optimisation methods such as stochastic…

We define a derived enhancement of the classical quot functor of quotients associated to a coherent sheaf on a nonsingular quasiprojective variety. We prove its representability and show that it has the expected tangent complex. The derived…

The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…

In this book chapter, we briefly describe the main components that constitute the gradient descent method and its accelerated and stochastic variants. We aim at explaining these components from a mathematical point of view, including…

High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…

This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…

We propose an approach to 3D reconstruction via inverse procedural modeling and investigate two variants of this approach. The first option consists in the fitting set of input parameters using a genetic algorithm. We demonstrate the…

In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…

Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…

This paper develops a general approach to characterize the long-time trajectory behavior of nonconvex gradient descent in generalized single-index models in the large aspect ratio regime. In this regime, we show that for each iteration the…

We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily…

We present an extended range of stable flux reconstruction (FR) methods on triangles through the development and application of the summation-by-parts framework in two-dimensions. This extended range of stable schemes is then shown to…

The Cartesian reverse derivative is a categorical generalization of reverse-mode automatic differentiation. We use this operator to generalize several optimization algorithms, including a straightforward generalization of gradient descent…

The generation of high-quality staggered unstructured grids is considered, leading to the development of a new optimisation-based strategy designed to construct weighted `Regular-Power' tessellations appropriate for co-volume type numerical…

In this text, we outline a theory of schemes associated with a site, which generalizes a variety of geometries, such as manifolds, schemes, analytic spaces, simplicial complexes, and more. We present an abstract process of gluing model…

In this paper, we propose a class of stochastic exponential discrete gradient schemes for SDEs with linear and gradient components in the coefficients. The root mean-square errors of the schemes are analyzed, and the structure-preserving…

We propose a new unified framework for describing and designing gradient-based convex optimization methods from a numerical analysis perspective. There the key is the new concept of weak discrete gradients (weak DGs), which is a…