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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

In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or may not have optimal Lagrange multipliers that close the…

Optimization and Control · Mathematics 2017-03-24 Ion Necoara , Andrei Patrascu , Francois Glineur

In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…

Optimization and Control · Mathematics 2025-03-04 Lahcen El Bourkhissi , Ion Necoara

In many real-world problems, first-order (FO) derivative evaluations are too expensive or even inaccessible. For solving these problems, zeroth-order (ZO) methods that only need function evaluations are often more efficient than FO methods…

Optimization and Control · Mathematics 2021-12-22 Zichong Li , Pin-Yu Chen , Sijia Liu , Songtao Lu , Yangyang Xu

This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…

Optimization and Control · Mathematics 2026-05-06 Yule Zhang , Benqi Liu , Xiantao Xiao , Liwei Zhang

In this paper, we study a class of convex composite optimization problems. We begin by characterizing the equivalence between the primal/dual strong second-order sufficient condition and the dual/primal nondegeneracy condition. Building on…

Optimization and Control · Mathematics 2025-07-18 Chengjing Wang , Peipei Tang

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

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

In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…

Optimization and Control · Mathematics 2023-05-09 Jie Liu , Xiaoqing Ou , Jiawei Chen

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

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

In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for…

Optimization and Control · Mathematics 2018-03-30 Ya-Feng Liu , Xin Liu , Shiqian Ma

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 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

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 method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original…

Optimization and Control · Mathematics 2020-04-16 Dusan Jakovetic , Dragana Bajovic , Joao Xavier , Jose M. F. Moura

In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax…

Optimization and Control · Mathematics 2026-01-06 Zhaosong Lu , Sanyou Mei

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

Optimization and Control · Mathematics 2020-12-02 Qihang Lin , Runchao Ma , Yangyang Xu

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

Recently, structure learning of directed acyclic graphs (DAGs) has been formulated as a continuous optimization problem by leveraging an algebraic characterization of acyclicity. The constrained problem is solved using the augmented…

Machine Learning · Computer Science 2022-04-12 Ignavier Ng , Sébastien Lachapelle , Nan Rosemary Ke , Simon Lacoste-Julien , Kun Zhang