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We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…

Optimization and Control · Mathematics 2020-04-02 Ben Hermans , Andreas Themelis , Panagiotis Patrinos

This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex…

Optimization and Control · Mathematics 2022-10-07 Arnesh Sujanani , Renato D. C. Monteiro

The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…

Optimization and Control · Mathematics 2015-11-30 Hung Nien , Jeffrey A. Fessler

Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In…

Optimization and Control · Mathematics 2022-12-20 Zichong Li , Pin-Yu Chen , Sijia Liu , Songtao Lu , Yangyang Xu

In this paper, we consider large-scale linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose a scalable \textbf{F}rank-\textbf{W}olfe based…

Optimization and Control · Mathematics 2015-10-13 Ya-Feng Liu , Xiangfeng Wang , Xin Liu , Shiqian Ma

In this paper we consider a class of convex conic programming. In particular, we first propose an inexact augmented Lagrangian (I-AL) method that resembles the classical I-AL method for solving this problem, in which the augmented…

Optimization and Control · Mathematics 2022-11-22 Zhaosong Lu , Zirui Zhou

We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…

Optimization and Control · Mathematics 2023-06-21 Jong Gwang Kim

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

Optimization and Control · Mathematics 2022-04-20 Xiaoxi Jia , Christian Kanzow , Patrick Mehlitz , Gerd Wachsmuth

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

The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…

Optimization and Control · Mathematics 2015-11-18 Canyi Lu , Huan Li , Zhouchen Lin , Shuicheng Yan

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

Optimization and Control · Mathematics 2026-02-23 Matthew X. Burns , Jiaming Liang

In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…

Optimization and Control · Mathematics 2025-05-08 Lahcen El Bourkhissi , Ion Necoara

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 consider a class of structured nonsmooth difference-of-convex (DC) constrained DC program in which the first convex component of the objective and constraints is the sum of a smooth and nonsmooth functions while their…

Optimization and Control · Mathematics 2021-11-18 Zhaosong Lu , Zhe Sun , Zirui Zhou

We consider the convex minimization model with both linear equality and inequality constraints, and reshape the classic augmented Lagrangian method (ALM) by balancing its subproblems. As a result, one of its subproblems decouples the…

Optimization and Control · Mathematics 2021-08-20 Bingsheng He , Xiaoming Yuan

We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the…

Optimization and Control · Mathematics 2020-09-15 Martin P. Neuenhofen , Eric C. Kerrigan

Symmetric cone programming covers a broad class of convex optimization problems, including linear programming, second-order cone programming, and semidefinite programming. Although the augmented Lagrangian method (ALM) is well-suited for…

Optimization and Control · Mathematics 2026-03-03 Rui-Jin Zhang , Ruoyu Diao , Xin-Wei Liu , Yu-Hong Dai

This paper provides a local convergence analysis of the proximal augmented Lagrangian method (PALM) applied to a class of non-convex conic programming problems. Previous convergence results for PALM typically imposed assumptions such as…

Optimization and Control · Mathematics 2025-09-16 Ning Zhang , Yi Zhang

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

Optimization and Control · Mathematics 2023-02-09 Alberto De Marchi , Xiaoxi Jia , Christian Kanzow , Patrick Mehlitz

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