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We study the fully mixed formulation of the Biot equations, which is characterized by a symmetric coupling between flow and deformation. This structure enables the use of stable mixed finite elements for each subproblem without a strong…

Numerical Analysis · Mathematics 2026-03-20 Fleurianne Bertrand , Jakub Wiktor Both , Tugay Dağlı

We study acceleration and preconditioning strategies for a class of Douglas-Rachford methods aiming at the solution of convex-concave saddle-point problems associated with Fenchel-Rockafellar duality. While the basic iteration converges…

Optimization and Control · Mathematics 2016-04-22 Kristian Bredies , Hongpeng Sun

In this paper, we propose a generalized shift-splitting (GSS) preconditioner, along with its two relaxed variants to solve the double saddle point problem (DSPP). The convergence of the associated GSS iterative method is analyzed, and…

Numerical Analysis · Mathematics 2025-07-08 Sk. Safique Ahmad , Pinki Khatun

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

We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…

Optimization and Control · Mathematics 2022-06-14 Ahmet Alacaoglu , Yura Malitsky

This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…

Optimization and Control · Mathematics 2022-11-15 Killian Wood , Emiliano Dall'Anese

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

We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…

Numerical Analysis · Mathematics 2021-09-13 Hamed Aslani , Davod Khojasteh Salkuyeh , Fatemeh Panjeh Ali Beik

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the…

Numerical Analysis · Mathematics 2016-08-24 M. Cai , A. J. Nonaka , J. B. Bell , B. E. Griffith , A. Donev

In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…

Optimization and Control · Mathematics 2024-10-16 Luke Fina , Christopher Petersen , Matthew Hale

We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…

Machine Learning · Computer Science 2019-09-17 Luo Luo , Cheng Chen , Yujun Li , Guangzeng Xie , Zhihua Zhang

In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…

Numerical Analysis · Mathematics 2015-03-05 Huidong Yang

We present and analyze a class of nonsymmetric preconditioners within a normal (weighted least-squares) matrix form for use in GMRES to solve nonsymmetric matrix problems that typically arise in finite element discretizations. An example of…

Numerical Analysis · Mathematics 2014-09-02 Blanca Ayuso de Dios , Andrew T. Barker , Panayot S. Vassilevski

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…

Machine Learning · Statistics 2015-06-15 Zhanxing Zhu , Amos J. Storkey

While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims…

Data Structures and Algorithms · Computer Science 2021-02-15 Anne-Elisabeth Falq , Pierre Fouilhoux , Safia Kedad-Sidhoum

In this paper, a fast solver is studied for saddle point system arising from a second-order Crank-Nicolson discretization of an initial-valued parabolic PDE constrained optimal control problem, which is indefinite and ill-conditioned.…

Numerical Analysis · Mathematics 2023-12-21 Xue-Lei Lin , Shu-Lin Wu

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…

Optimization and Control · Mathematics 2024-05-20 Gabriele Ciaramella , Fabio Nobile , Tommaso Vanzan

A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational…

Numerical Analysis · Mathematics 2010-01-12 Michael Holst , Stefan Vandewalle

High-index saddle dynamics (HiSD) is an effective approach for computing saddle points of a prescribed Morse index and constructing solution landscapes for complex nonlinear systems. However, for problems with ill-conditioned Hessians…

Numerical Analysis · Mathematics 2026-05-25 Bingzhang Huang , Hua Su , Lei Zhang , Jin Zhao

Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics…

Artificial Intelligence · Computer Science 2013-09-27 Luis Gustavo Vianna , Scott Sanner , Leliane Nunes de Barros