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In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. In this paper, we propose a fast algorithm using a simulation-extrapolation…
The cross-entropy (CE) method is a popular stochastic method for optimization due to its simplicity and effectiveness. Designed for rare-event simulations where the probability of a target event occurring is relatively small, the CE-method…
This paper presents comparison of several stochastic optimization algorithms developed by authors in their previous works for the solution of some problems arising in Civil Engineering. The introduced optimization methods are: the integer…
This paper studies distributed estimation and inference for a general statistical problem with a convex loss that could be non-differentiable. For the purpose of efficient computation, we restrict ourselves to stochastic first-order…
In this article, we present an overview of different a posteriori error analysis and postprocessing methods proposed in the context of nonlinear eigenvalue problems, e.g. arising inelectronic structure calculations for the calculation of…
Recently, Nystr\"{o}m method has proved its prominence empirically and theoretically in speeding up the training of kernel machines while retaining satisfactory performances and accuracy. So far, there are several different approaches…
Evolution strategies (ESs) are zeroth-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are…
In this paper, we present an error analysis of one-stage explicit extended Runge--Kutta--Nystr\"{o}m integrators for semilinear wave equations. These equations are analysed by using spatial semidiscretizations with periodic boundary…
Sustained oscillations (SOs) are commonly observed in systems dominated by converters. Under specific conditions, even though the origin of SOs can be identified through negative damping modes using conventional linear analysis, utilizing…
The convergence behaviour of first-order methods can be severely slowed down when applied to high-dimensional non-convex functions due to the presence of saddle points. If, additionally, the saddles are surrounded by large plateaus, it is…
Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the…
Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of…
Feature detection is an important procedure for image matching, where unsupervised feature detection methods are the detection approaches that have been mostly studied recently, including the ones that are based on repeatability requirement…
This work considers the decentralized successive convex approximation (SCA) method for minimizing stochastic non-convex objectives subject to convex constraints, along with possibly non-smooth convex regularizers. Although SCA has been…
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…
This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…
The center-bias (or zero-bias) operator has recently been identified as one of the problems plaguing the benchmarking of evolutionary computation methods. This operator lets the methods that utilize it easily optimize functions that have…
Randomized algorithms in numerical linear algebra have proven to be effective in ameliorating issues of scalability when working with large matrices, efficiently producing accurate low-rank approximations. A key remaining challenge,…
In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. We will show that the augmented subspace methods have the second order convergence rate which is…
We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Based on the newly derived distorted…