Related papers: An inexact Picard iteration method for absolute va…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence…
We consider the generalized Newton method (GNM) for the absolute value equation (AVE) $Ax-|x|=b$. The method has finite termination property whenever it is convergent, no matter whether the AVE has a unique solution. We prove that GNM is…
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several…
This research investigates using a mixed-precision iterative refinement method using posit numbers instead of the standard IEEE floating-point format. The method is applied to solve a general linear system represented by the equation $Ax =…
A procedure is suggested for testing the resolution and comparing the relative accuracy of numerical schemes for integration of the incompressible Euler equations.
Often in real-world datasets, especially in high dimensional data, some feature values are missing. Since most data analysis and statistical methods do not handle gracefully missing values, the first step in the analysis requires the…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
We introduce a new approach to obtaining pointwise estimates for solutions of elliptic boundary value problems when the operator being considered satisfies a certain type of weighted integral inequalities. The method is illustrated on…
We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
In this paper we introduce a multilevel Picard approximation algorithm for semilinear parabolic partial integro-differential equations (PIDEs). We prove that the numerical approximation scheme converges to the unique viscosity solution of…
Iterative imputation is a popular tool to accommodate missing data. While it is widely accepted that valid inferences can be obtained with this technique, these inferences all rely on algorithmic convergence. There is no consensus on how to…
We construct two optimal Newton-Secant like iterative methods for solving non-linear equations. The proposed classes have convergence order four and eight and cost only three and four function evaluations per iteration, respectively. These…
A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of…
Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to…
Since there exist several completion methods to estimate the missing entries of pairwise comparison matrices, practitioners face a difficult task in choosing the best technique. Our paper contributes to this issue: we consider a special set…
Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solution of the large matrix eigenvalue problems arising from…
Aussel et al. (J Optim Theory Appl 170 818-837 2016) introduced the concept of projected solutions for the quasi-variational inequalities with a non-self constraint map, that is, the case where the constraint map may take values outside the…
Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…
The need to estimate a positive definite solution to an overdetermined linear system of equations with multiple right hand side vectors arises in several process control contexts. The coefficient and the right hand side matrices are…