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In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming…

Numerical Analysis · Mathematics 2024-02-13 Qiya Hu , Ziyi Li

A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear…

Optimization and Control · Mathematics 2022-01-10 Frank E. Curtis , Michael J. O'Neill , Daniel P. Robinson

Pricing American options is more complicated than pricing European options, because they can be exercised at any time, and one thus needs to solve a linear complementarity problem instead of simply doing time stepping for computing European…

Numerical Analysis · Mathematics 2026-05-22 Martin J. Gande , Si-Wei Liao , Liu-Di Lu

The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…

Optimization and Control · Mathematics 2024-12-30 Soodeh Habibi , Michal Kocvara , Michael Stingl

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

Machine Learning · Computer Science 2021-11-23 Kai Yan , Jie Yan , Chuan Luo , Liting Chen , Qingwei Lin , Dongmei Zhang

This work focuses on the development of a two-step field-split nonlinear preconditioner to accelerate the convergence of two-phase flow and transport in heterogeneous porous media. We propose a field-split algorithm named Field-Split…

Numerical Analysis · Mathematics 2023-03-06 Mamadou N'diaye , Francois P. Hamon , Hamdi A. Tchelepi

We investigate additive Schwarz methods for semilinear elliptic problems with convex energy functionals, which have wide scientific applications. A key observation is that the convergence rates of both one- and two-level additive Schwarz…

Numerical Analysis · Mathematics 2024-07-09 Jongho Park

We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…

Numerical Analysis · Mathematics 2019-12-20 Carlos Echeverría , Jörg Liesen , Petr Tichý

A thermo-elastoplastic finite element approach is used to perform the simulation of a laser beam welding (LBW) process. This results in a nonlinear, nonsymmetric saddle point multiphysics system, for which the nonlinearity is handled via…

Numerical Analysis · Mathematics 2025-02-28 Tommaso Bevilacqua , Axel Klawonn , Martin Lanser

We derive an extension of the sequential homotopy method that allows for the application of inexact solvers for the linear (double) saddle-point systems arising in the local semismooth Newton method for the homotopy subproblems. For the…

Optimization and Control · Mathematics 2023-11-30 John W. Pearson , Andreas Potschka

In this paper, we extend the additive average Schwarz method to solve second order elliptic boundary value problems with heterogeneous coefficients inside the subdomains and across their interfaces by the mortar technique, where the mortar…

Numerical Analysis · Mathematics 2021-02-11 Ali Khademi , Leszek Marcinkowski , Sanjib Kumar Acharya , Talal Rahman

First-order conic optimization solvers are sensitive to problem conditioning and typically perform poorly in the face of ill-conditioned problem data. To mitigate this, we propose an approach to preconditioning--the hypersphere…

Optimization and Control · Mathematics 2025-04-29 Abhinav G. Kamath , Purnanand Elango , Behçet Açıkmeşe

We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations…

Optimization and Control · Mathematics 2026-04-17 Figen Oztoprak , Richard Byrd

This article is concerned with the question of constructing effcient multigrid preconditioners for the linear systems arising when applying semismooth Newton methods to large-scale linear-quadratic optimization problems constrained by…

Numerical Analysis · Mathematics 2013-11-08 Andrei Draganescu

Monolithic preconditioners applied to the linear systems arising during the solution of the discretized incompressible Navier-Stokes equations are typically more robust than preconditioners based on incomplete block factorizations. Lower…

Numerical Analysis · Mathematics 2026-02-11 Alexander Heinlein , Axel Klawonn , Jascha Knepper , Lea Saßmannshausen

The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…

Numerical Analysis · Mathematics 2016-11-03 Mingchao Cai , Luca F. Pavarino

Schwarz methods use a decomposition of the computational domain into subdomains and need to put boundary conditions on the subdomain boundaries. In domain truncation one restricts the unbounded domain to a bounded computational domain and…

Numerical Analysis · Mathematics 2022-07-21 Martin J. Gander , Hui Zhang

Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equations. We consider the case of the Stokes equations…

Numerical Analysis · Mathematics 2025-12-02 Filipe Cumaru , Alexander Heinlein , Joachim Schöberl

In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine…

Numerical Analysis · Mathematics 2015-09-23 Yiming Bu , Bruno Carpentieri , Zhaoli Shen , Tingzhu Huang

We analyze a multilevel diagonal additive Schwarz preconditioner for the adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem. We rigorously prove that the condition number of the preconditioned system stays…

Numerical Analysis · Mathematics 2017-12-04 Michael Feischl , Thomas Führer , Dirk Praetorius , Ernst P. Stephan