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In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…

Optimization and Control · Mathematics 2017-01-25 Xiang Gao , Yangyang Xu , Shuzhong Zhang

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

Optimization and Control · Mathematics 2024-03-05 Xueyi Bu , Brian Plancher

In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic…

Optimization and Control · Mathematics 2023-10-27 Shahriar Talebi , Mehran Mesbahi

We introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control…

Optimization and Control · Mathematics 2021-04-02 Gabriele Ciaramella , Felix Kwok , Georg Müller

We consider the eigenvalue problem for the Schr\"odinger operator on bounded, convex domains with mixed boundary conditions, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its…

Spectral Theory · Mathematics 2024-09-04 Nausica Aldeghi

In this experimental work, we present a general framework based on the Bregman log determinant divergence for preconditioning Hermitian positive definite linear systems. We explore this divergence as a measure of discrepancy between a…

Numerical Analysis · Mathematics 2024-10-10 Andreas A. Bock , Martin S. Andersen

We consider a nonlinear eigenvalue problem (NEP) arising from absorbing boundary conditions in the study of a partial differential equation (PDE) describing a waveguide. We propose a new computational approach for this large scale NEP based…

Numerical Analysis · Mathematics 2017-10-27 Emil Ringh , Giampaolo Mele , Johan Karlsson , Elias Jarlebring

This work is concerned with the convergence of the iterative solution for the Stokes flow, discretized with the weak Galerkin finite element method and preconditioned using inexact block Schur complement preconditioning. The resulting…

Numerical Analysis · Mathematics 2024-09-26 Weizhang Huang , Zhuoran Wang

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…

This paper proposes a provably convergent multiblock ADMM for nonconvex optimization with nonlinear dynamics constraints, overcoming the divergence issue in classical extensions. We consider a class of optimization problems that arise from…

Optimization and Control · Mathematics 2025-06-24 Bowen Li , Ya-xiang Yuan

We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. We discuss the spectral properties associated to a weighted eigenvalue problem and present a global bound for subsolutions. The Neumann…

Analysis of PDEs · Mathematics 2020-06-09 Serena Dipierro , Edoardo Proietti Lippi , Enrico Valdinoci

We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated,…

Numerical Analysis · Mathematics 2015-09-01 Paolo Gatto , Jan S. Hesthaven

This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…

Numerical Analysis · Mathematics 2018-08-03 Yuliya Gorb , Vasiliy Kramarenko , Yuri Kuznetsov

PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically…

Numerical Analysis · Mathematics 2016-11-23 Margherita Porcelli , Valeria Simoncini , Martin Stoll

In this work, we consider the modeling of inclusions in the material using an unfitted finite element method. In the unfitted methods, structured background meshes are used and only the underlying finite element space is modified to…

Numerical Analysis · Mathematics 2021-03-26 Hardik Kothari , Rolf Krause

A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…

Numerical Analysis · Mathematics 2018-01-08 Yuliya Gorb , Daria Kurzanova , Yuri Kuznetsov

This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we…

Analysis of PDEs · Mathematics 2026-04-28 Debajyoti Choudhuri , Dušan D. Repovš , Kamel Saoudi

We study the stability of the two-dimensional Lax-Wendroff scheme with a stabilizer that approximates solutions to the transport equation. The problem is first analyzed in the whole space in order to show that the so-called energy method…

Numerical Analysis · Mathematics 2022-10-12 Jean-François Coulombel , Antoine Benoit

In this paper, we develop a novel primal-dual semismooth Newton method for solving linearly constrained multi-block convex composite optimization problems. First, a differentiable augmented Lagrangian (AL) function is constructed by…

Optimization and Control · Mathematics 2024-05-17 Zhanwang Deng , Kangkang Deng , Jiang Hu , Zaiwen Wen

This paper proposes a new preconditioning scheme for a linear system with a saddle-point structure arising from a hybrid approximation scheme on the sphere, an approximation scheme that combines (local) spherical radial basis functions and…

Numerical Analysis · Mathematics 2010-09-23 Q. T. Le Gia , Ian H. Sloan , Andrew J. Wathen