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Augmented Lagrangian (AL) methods are a well known class of algorithms for solving constrained optimization problems. They have been extended to the solution of saddle-point systems of linear equations. We study an AL (SPAL) algorithm for…

Numerical Analysis · Mathematics 2024-04-24 N. Huang , Y. -H. Dai , D. Orban , M. A. Saunders

Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence…

Optimization and Control · Mathematics 2018-03-28 Yangyang Xu

In this paper we present complexity certification results for a distributed Augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the Accelerated…

Optimization and Control · Mathematics 2018-01-16 Soomin Lee , Nikolaos Chatzipanagiotis , Michael M. Zavlanos

In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…

Optimization and Control · Mathematics 2015-05-14 Andrei Patrascu , Ion Necoara , Quoc Tran-Dinh

We design inexact proximal augmented Lagrangian based decomposition methods for convex composite programming problems with dual block-angular structures. Our methods are particularly well suited for convex quadratic programming problems…

Optimization and Control · Mathematics 2023-03-14 Kuang-Yu Ding , Xin-Yee Lam , Kim-Chuan Toh

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

In this paper, we propose an adaptive proximal inexact gradient (APIG) framework for solving a class of nonsmooth composite optimization problems involving function and gradient errors. Unlike existing inexact proximal gradient methods, the…

Information Theory · Computer Science 2025-04-03 Xilai Fan , Bo Jiang , Ya-Feng Liu

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

Physics and equality constrained artificial neural networks (PECANN) are grounded in methods of constrained optimization to properly constrain the solution of partial differential equations (PDEs) with their boundary and initial conditions…

Machine Learning · Computer Science 2023-07-18 Shamsulhaq Basir , Inanc Senocak

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

Optimization and Control · Mathematics 2025-03-04 Lahcen El Bourkhissi , Ion Necoara , Panagiotis Patrinos , Quoc Tran-Dinh

This article investigates the convergence properties of a relative-type inexact preconditioned proximal augmented Lagrangian method (rip$^2$ALM) for convex nonlinear programming, a fundamental class of optimization problems with broad…

Optimization and Control · Mathematics 2026-03-31 Lei Yang , Jiayi Zhu , Ling Liang , Kim-Chuan Toh

The Augmented Lagrangian Method (ALM) is an iterative method for the solution of equality-constrained non-linear programming problems. In contrast to the quadratic penalty method, the ALM can satisfy equality constraints in an exact way.…

Numerical Analysis · Mathematics 2018-04-24 Martin Neuenhofen

Inexact proximal augmented Lagrangian methods (ipALMs) have been widely used for solving linearly constrained convex optimization problems, owing to their strong theoretical guarantees and excellent numerical performance. In practice,…

Optimization and Control · Mathematics 2026-05-08 Jiayi Zhu , Ling Liang , Lei Yang , Kim-Chuan Toh

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Numerical Analysis · Mathematics 2025-06-16 Jianchao Bai , Linyuan Jia , Zheng Peng

The augmented Lagrangian method (ALM) is one of the most useful methods for constrained optimization. Its convergence has been well established under convexity assumptions or smoothness assumptions, or under both assumptions. ALM may…

Optimization and Control · Mathematics 2021-12-10 Jinshan Zeng , Wotao Yin , Ding-Xuan Zhou

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is…

Optimization and Control · Mathematics 2022-04-22 Mehmet Fatih Sahin , Armin Eftekhari , Ahmet Alacaoglu , Fabian Latorre , Volkan Cevher

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…

Optimization and Control · Mathematics 2023-05-31 Ilgee Hong , Sen Na , Michael W. Mahoney , Mladen Kolar

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…

Optimization and Control · Mathematics 2023-12-29 Raghu Bollapragada , Cem Karamanli , Brendan Keith , Boyan Lazarov , Socratis Petrides , Jingyi Wang

We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…

Optimization and Control · Mathematics 2021-08-16 Martin Neuenhofen , Eric Kerrigan

We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a nested double-loop structure, our framework features a…

Optimization and Control · Mathematics 2025-02-14 Feng-Yi Liao , Yang Zheng