Related papers: IDEAL: Inexact DEcentralized Accelerated Augmented…
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…
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…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity…
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…
This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…
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…
This paper presents two new techniques relating to inexact solution of subproblems in augmented Lagrangian methods for convex programming. The first involves combining a relative error criterion for solution of the subproblems with over- or…
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…
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…
We develop a new inexact interior-point Lagrangian decomposition method to solve a wide range class of constrained composite convex optimization problems. Our method relies on four techniques: Lagrangian dual decomposition, self-concordant…
In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
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…
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…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
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…
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…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…