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This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…

Numerical Analysis · Mathematics 2022-05-10 Jianguo Huang , Haoqin Wang , Tao Zhou

This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…

Optimization and Control · Mathematics 2024-10-07 José Luis Romero , Damián Fernandez , Germán Ariel Torres

We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…

Optimization and Control · Mathematics 2018-06-15 Quoc Tran-Dinh , Yuzixuan Zhu

In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and some candidate image on a large collection of subboxes. The…

Optimization and Control · Mathematics 2024-06-24 Christian Kanzow , Fabius Krämer , Patrick Mehlitz , Gerd Wachsmuth , Frank Werner

We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the…

Optimization and Control · Mathematics 2026-01-21 Young-Ju Lee , Jongho Park

We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the…

Numerical Analysis · Mathematics 2016-09-13 Erik Burman , Peter Hansbo , Mats Larson

In this paper, we show that Chen-Teboulle's proximal-based decomposition method can be interpreted as a proximal augmented Lagrangian method. More precisely, it coincides with a linearized augmented Lagrangian method. We then proposed three…

Optimization and Control · Mathematics 2020-06-22 Feng Ma

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…

Optimization and Control · Mathematics 2018-09-12 Marianna De Santis , Franz Rendl , Angelika Wiegele

To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is…

Optimization and Control · Mathematics 2021-11-16 Bin Gao , Xin Liu , Ya-xiang Yuan

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

Optimization and Control · Mathematics 2014-12-16 Marc Toussaint

This work introduces an unconventional inexact augmented Lagrangian method where the augmenting term is a Euclidean norm raised to a power between one and two. The proposed algorithm is applicable to a broad class of constrained nonconvex…

Optimization and Control · Mathematics 2025-11-25 Alexander Bodard , Konstantinos Oikonomidis , Emanuel Laude , Panagiotis Patrinos

This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization…

Optimization and Control · Mathematics 2026-03-17 Roland Andrews , Justin Carpentier , Adrien Taylor

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…

Numerical Analysis · Mathematics 2015-06-04 Klaus Frick , Markus Grasmair

Dual decomposition is a powerful technique for deriving decomposition schemes for convex optimization problems with separable structure. Although the Augmented Lagrangian is computationally more stable than the ordinary Lagrangian, the…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Johan A. K. Suykens

Within the framework of the augmented Lagrangian (AL), we propose a novel distributed optimization method, termed Distributed Augmented Lagrangian Decomposition (DALD), and provide a rigorous convergence proof for its standard version. To…

Optimization and Control · Mathematics 2025-10-07 Wenyou Guo , Ting Qu , Hainan Huang , Yafeng Wei

We consider the augmented Lagrangian method (ALM) as a solver for the fused lasso signal approximator (FLSA) problem. The ALM is a dual method in which squares of the constraint functions are added as penalties to the Lagrangian. In order…

Computation · Statistics 2010-05-28 Heng Lian

We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture…

Optimization and Control · Mathematics 2024-12-02 Dan Greenstein , Nadav Hallak

There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…

Optimization and Control · Mathematics 2021-11-12 Yu-Hong Dai , Liwei Zhang

The objective of this paper is to introduce and demonstrate a robust methodology for solving multi-constrained 3D topology optimization problems. The proposed methodology is a combination of the topological level-set formulation, augmented…

Computational Engineering, Finance, and Science · Computer Science 2022-03-31 Shiguang Deng , Suresh Krishnan

This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…

Optimization and Control · Mathematics 2025-11-11 Alberto De Marchi , Tim Hoheisel , Patrick Mehlitz