Related papers: Complexity of a linearized augmented Lagrangian me…
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…
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…
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…
Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…
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…
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…
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…
In this paper, we consider nonconvex optimization problems with nonlinear equality constraints. We assume that the objective function and the functional constraints are locally smooth. To solve this problem, we introduce a linearized…
This paper considers smooth convex optimization problems with many functional constraints. To solve this general class of problems we propose a new stochastic perturbed augmented Lagrangian method, called SGDPA, where a perturbation is…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…
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…