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In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting of a large number of linear equality, inequality…

Optimization and Control · Mathematics 2017-01-02 Xudong Li , Defeng Sun , Kim-Chuan Toh

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 paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…

Optimization and Control · Mathematics 2026-05-11 Lixin Tang , Xingyu Wang , Liwei Zhang

First-order methods (FOMs) have been widely used for solving large-scale problems. A majority of existing works focus on problems without constraint or with simple constraints. Several recent works have studied FOMs for problems with…

Optimization and Control · Mathematics 2021-02-10 Zichong Li , Yangyang Xu

We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…

Optimization and Control · Mathematics 2018-04-09 Joachim Giesen , Sören Laue

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with joint feasibility constraints and expected-value cost functions. We propose a distributed stochastic projected reflected gradient algorithm and show its almost…

Optimization and Control · Mathematics 2021-03-22 Barbara Franci , Sergio Grammatico

Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the…

Machine Learning · Computer Science 2025-10-30 Ignacio Boero , Ignacio Hounie , Alejandro Ribeiro

We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward-backward operator…

Optimization and Control · Mathematics 2020-02-17 Barbara Franci , Sergio Grammatico

We propose a duality scheme for solving constrained nonsmooth and nonconvex optimization problems in a reflexive Banach space. We establish strong duality for a very general type of augmented Lagrangian, in which we assume a less…

Optimization and Control · Mathematics 2023-02-07 Regina S. Burachik , Xuemei Liu

This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such problems considered in both exact and inexact…

Optimization and Control · Mathematics 2021-07-07 Nguyen T. V. Hang , Boris S. Mordukhovich , M. Ebrahim Sarabi

NashOpt is an open-source Python library for computing and designing generalized Nash equilibria (GNEs) in noncooperative games with shared constraints and real-valued decision variables. The library exploits the joint Karush-Kuhn-Tucker…

Systems and Control · Electrical Eng. & Systems 2026-03-19 Alberto Bemporad

This paper proposes D-ripALM, a Decentralized relative-type inexact proximal Augmented Lagrangian Method for consensus convex optimization over multi-agent networks. D-ripALM adopts a double-loop distributed optimization framework that…

Optimization and Control · Mathematics 2026-02-09 Jiayi Zhu , Hong Wang , Ling Liang , Lei Yang

In the article we present a general theory of augmented Lagrangian functions for cone constrained optimization problems that allows one to study almost all known augmented Lagrangians for cone constrained programs within a unified…

Optimization and Control · Mathematics 2024-09-11 M. V. Dolgopolik

We propose two basic assumptions, under which the rate of convergence of the augmented Lagrange method for a class of composite optimization problems is estimated. We analyze the rate of local convergence of the augmented Lagrangian method…

Optimization and Control · Mathematics 2017-09-05 Liwei Zhang , Yule Zhang , Jia Wu

In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…

Optimization and Control · Mathematics 2018-10-31 Han Zhang , Jieqiang Wei , Peng Yi , Xiaoming Hu

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

Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie…

Robotics · Computer Science 2022-10-06 Wilson Jallet , Antoine Bambade , Nicolas Mansard , Justin Carpentier

In this paper, we present a relaxation proximal point method with double inertial effects to approximate a solution of a non-convex equilibrium problem. We give global convergence results of the iterative sequence generated by our…

Optimization and Control · Mathematics 2025-02-18 Nam Van Tran

We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically,…

Numerical Analysis · Mathematics 2026-02-06 Jan Bohn , Willy Dörfler , Michael Feischl , Stefan Karch

This paper investigates stochastic generalized dynamic games with coupling chance constraints, where agents have incomplete information about uncertainties satisfying a concentration of measure property. This problem, in general, is…

Systems and Control · Electrical Eng. & Systems 2026-02-06 Seyed Shahram Yadollahi , Hamed Kebriaei , Sadegh Soudjani