Related papers: A parallelizable augmented Lagrangian method appli…
Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and…
In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints.We investigate the…
We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…
Lagrangian-based methods are classical methods for solving convex optimization problems with equality constraints. We present novel prediction-correction frameworks for such methods and their variants, which can achieve $O(1/k)$ non-ergodic…
This paper proposes a novel first-order algorithm that solves composite nonsmooth and stochastic convex optimization problem with function constraints. Most of the works in the literature provide convergence rate guarantees on the…
This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…
This paper proposes a provably convergent multiblock ADMM for nonconvex optimization with nonlinear dynamics constraints, overcoming the divergence issue in classical extensions. We consider a class of optimization problems that arise from…
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…
Unsupervised feature selection has drawn wide attention in the era of big data since it is a primary technique for dimensionality reduction. However, many existing unsupervised feature selection models and solution methods were presented…
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,…
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…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…
This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual…
We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In…
We give a damped proximal augmented Lagrangian method (DPALM) for solving problems with a weakly-convex objective and convex linear/nonlinear constraints. Instead of taking a full stepsize, DPALM adopts a damped dual stepsize to ensure the…
The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Many problems in machine learning and other fields can be (re)for-mulated as linearly constrained separable convex programs. In most of the cases, there are multiple blocks of variables. However, the traditional alternating direction method…
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…