In this paper, we consider stochastic composite convex optimization problems with the objective function satisfying a bounded gradient condition, or without quadratic functional growth property. These models include most well-known classes of functions analyzed in literature: nonsmooth Lipschitz and composition (potentially) smooth function, strong convexity. Based on flexibility offered by our...

This paper is concerned with the time discretization of nonlinear evolution equations. We work in an abstract Banach space setting of analytic semigroups that covers fully nonlinear parabolic initial-boundary value problems with smooth coefficients. We prove convergence of variable stepsize backward Euler discretizations under various smoothness assumptions on the exact solution. We further sho...

We propose a simple and quite efficient code to solve singular perturbation problems when the perturbation parameter ǫ is very small. The code is based on generalized upwind methods of order ranging from 4 to 10 and uses highly variable stepsize to fit the boundary regions with relatively few points. An extensive numerical test section shows the effectiveness of the proposed technique on linear...

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

Conjugate gradient methods are efficient methods for minimizing differentiable objective functions in large dimension spaces. However, converging line search strategies are usually not easy to choose, nor to implement. Sun and colleagues (Ann. Oper. Res. 103:161–173, 2001; J. Comput. Appl. Math. 146:37–45, 2002) introduced a simple stepsize formula. However, the associated convergence domain ha...

Unbiased interpretation of noisy single molecular motor recordings remains a challenging task. To address this issue, we have developed robust algorithms based on hidden Markov models (HMMs) of motor proteins. The basic algorithm, called variable-stepsize HMM (VS-HMM), was introduced in the previous article. It improves on currently available Markov-model based techniques by allowing for arbitr...

Abstract The numerical treatment of an atmospheric chemical scheme, which contains 56 species, is discussed in this paper. This scheme often used studies air pollution levels different domains, as, for example, Europe, by large-scale environmental models containing additionally two other important physical processes—transport pollutants the atmosphere (advection) and diffusion phenomena. We sha...

In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The uses variable stepsize which is updated at each iteration and based some previous iterates. convergence analysis of the proposed discussed under mild assumptions. case where bifunction strongly pseudomonotone, $R$-linear rate formulated. A fundamental experiment...

This paper proposes a new inertial triple-projection algorithm for solving the split feasibility problem. The process of projections is divided into three parts. Each part adopts different variable stepsize to obtain its projection point, which from existing extragradient methods. Flexible rules are employed selecting stepsizes and technique used improving convergence. Convergence results prove...