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We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of…

Numerical Analysis · Mathematics 2019-12-19 Philip K. Kristensen , Emilio Martínez-Pañeda

In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…

Optimization and Control · Mathematics 2025-05-21 K. Gupta , D. Ghosh , C. Tammer , X. Zhao , J. C. Yao

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for…

Optimization and Control · Mathematics 2025-10-14 Sebastian Blauth , Kevin Sturm

The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…

Optimization and Control · Mathematics 2024-01-24 David Ek , Anders Forsgren

In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true…

Optimization and Control · Mathematics 2021-03-26 Minghan Yang , Dong Xu , Hongyu Chen , Zaiwen Wen , Mengyun Chen

We present a first step towards a multigrid method for solving the min-cost flow problem. Specifically, we present a strategy that takes advantage of existing black-box fast iterative linear solvers, i.e. algebraic multigrid methods. We…

Optimization and Control · Mathematics 2016-12-02 Alessio Quaglino , Rolf Krause

Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other…

Optimization and Control · Mathematics 2021-02-09 Damien Scieur , Lewis Liu , Thomas Pumir , Nicolas Boumal

We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…

Fluid Dynamics · Physics 2018-03-14 Ravindra Pethiyagoda , Timothy J. Moroney , Scott W. McCue

An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure)…

Computational Physics · Physics 2007-05-23 Masato Ida

Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the…

Optimization and Control · Mathematics 2017-12-05 Oleg Burdakov , Ahmad Kamandi

Simulating compositional multiphase flow in porous media is a challenging task, especially when phase transition is taken into account. The main problem with phase transition stems from the inconsistency of the primary variables such as…

Numerical Analysis · Mathematics 2021-01-08 Q. M. Bui , H. C. Elman

This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…

Optimization and Control · Mathematics 2023-01-24 Nicolas F. Armijo , Yunier Bello-Cruz , Gabriel Haeser

In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…

Numerical Analysis · Mathematics 2023-10-31 Mirco Ciallella , Thomas Milcent

This work focuses on the derivation and the analysis of a novel, strongly-coupled partitioned method for fluid-structure interaction problems. The flow is assumed to be viscous and incompressible, and the structure is modeled using linear…

Numerical Analysis · Mathematics 2022-11-09 Martina Bukac , Anyastassia Seboldt , Catalin Trenchea

Coupled hydro-mechanical processes are of great importance to numerous engineering systems, e.g., hydraulic fracturing, geothermal energy, and carbon sequestration. Fluid flow in fractures is modeled after a Poiseuille law that relates the…

Computational Engineering, Finance, and Science · Computer Science 2021-11-02 Guotong Ren , Rami M. Younis

Designing efficient quasi-Newton methods is an important problem in nonlinear optimization and the solution of systems of nonlinear equations. From the perspective of the matrix approximation process, this paper presents a unified framework…

Optimization and Control · Mathematics 2025-08-15 Zhenyuan Ji

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…

Optimization and Control · Mathematics 2013-03-04 Stephen Becker , M. Jalal Fadili

This paper addresses the challenge of solving large-scale nonlinear equations with H\"older continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms…

Optimization and Control · Mathematics 2024-07-04 Zhiling Zhou , Zhuanghua Liu , Chengchang Liu , Luo Luo

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…

Optimization and Control · Mathematics 2023-03-22 Jiaojiao Zhang , Huikang Liu , Anthony Man-Cho So , Qing Ling

The cost of a partitioned fluid-structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the Newton loops within the nonlinear sub-solvers. In this work, we discuss why…

Numerical Analysis · Mathematics 2021-07-01 Thomas Spenke , Norbert Hosters , Marek Behr