相关论文: Splitting Method for Support Vector Machine with L…

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…

In this paper, we employ a global aggregate subgradient method for the numerical solution of hemivariational inequality problems arising in contact mechanics. The method integrates a global search procedure to identify starting points for a…

This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…

We show that the vanishing stepsize subgradient method -- widely adopted for machine learning applications -- can display rather messy behavior even in the presence of favorable assumptions. We establish that convergence of bounded…

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…

In this paper, we present a novel region-based segmentation method for cortical spreading depressions in 2-photon microscopy images. Fluorescent microscopy has become an important tool in neuroscience, but segmentation approaches are…

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…

We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…

The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…

Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…

We consider a 3-block Alternating Direction Method of Multipliers (ADMM) for solving nonconvex nonseparable problems with a linear constraint. Inspired by \cite[Sun, Toh and Yang, \textit{SIAM Journal on Optimization}, 25 (2015),…

Many imaging problems, such as total variation reconstruction of X-ray computed tomography (CT) and positron-emission tomography (PET), are solved via a convex optimization problem with near-circulant, but not actually circulant, linear…

Stochastic differentiable approximation schemes are widely used for solving high dimensional problems. Most of existing methods satisfy some desirable properties, including conditional descent inequalities, and almost sure (a.s.)…

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…

In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…

The purpose of this paper is to extend the full convergence results of the classic GLL-type (Grippo-Lampariello-Lucidi) nonmonotone methods to nonconvex and nonsmooth optimization. We propose a novel iterative framework for the minimization…

In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…

In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…