English
Related papers

Related papers: Complexity of a linearized augmented Lagrangian me…

200 papers

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

We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…

Optimization and Control · Mathematics 2025-09-09 M. V. Dolgopolik

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

Optimization and Control · Mathematics 2015-03-04 Quoc Tran-Dinh , Volkan Cevher

This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL method consists of: (i) inexactly…

Optimization and Control · Mathematics 2023-02-08 Weiwei Kong , Renato D. C. Monteiro

We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…

Optimization and Control · Mathematics 2023-11-03 Angelia Nedich , Tatiana Tatarenko

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

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…

Optimization and Control · Mathematics 2014-01-09 Anatoli Iouditski , Yuri Nesterov

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

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…

Optimization and Control · Mathematics 2024-04-12 Yutong Dai , Xiaoyi Qu , Daniel P. Robinson

This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal…

Optimization and Control · Mathematics 2022-06-16 Liwei Zhang , Yule Zhang , Jia Wu , Xiantao Xiao

Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…

Optimization and Control · Mathematics 2025-05-08 Danial Davarnia , Mohammadreza Kiaghadi

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

This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…

Optimization and Control · Mathematics 2018-03-28 Emanuel Laude , Daniel Cremers

We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…

Optimization and Control · Mathematics 2018-08-15 Quoc Tran-Dinh , Ahmet Alacaoglu , Olivier Fercoq , Volkan Cevher

Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…

Robotics · Computer Science 2018-03-13 Arun Kumar Singh , Reza Ghabcheloo , Andreas Muller , Harit Pandya

This paper presents a fully asynchronous and distributed approach for tackling optimization problems in which both the objective function and the constraints may be nonconvex. In the considered network setting each node is active upon…

Optimization and Control · Mathematics 2019-02-25 Francesco Farina , Andrea Garulli , Antonio Giannitrapani , Giuseppe Notarstefano

This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…

Optimization and Control · Mathematics 2024-10-15 Kenshiro Oguri

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

This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…

Optimization and Control · Mathematics 2024-11-25 Juan Liu , Nan-Jing Huang , Xian-Jun Long , Xue-song Li

In this paper, we consider the linear programming (LP) formulation for deep reinforcement learning. The number of the constraints depends on the size of state and action spaces, which makes the problem intractable in large or continuous…

Optimization and Control · Mathematics 2021-05-21 Yongfeng Li , Mingming Zhao , Weijie Chen , Zaiwen Wen