We propose an augmented Lagrangian algorithm for solving large-scale constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the core augment...

We propose a novel distributed method for convex optimization problems with a certain separability structure. The method is based on the augmented Lagrangian framework. We analyze its convergence and provide an application to two network models, as well as to a two-stage stochastic optimization problem. The proposed method compares favorably to two augmented Lagrangian decomposition methods kno...

In this paper, an algorithm for sparse learning via Maximum Margin Matrix Factorization(MMMF) is proposed. The algorithm is based on L1 penality and Alternating Direction Method of Multipliers. It shows that with sparse factors, sparse factors method can obtain result as good as dense factors.

This paper is devoted to the design of a decentralized optimal batch LQ state observer for state estimation of large-scale interconnected systems, well suited for implementation on a sensor network. The here-proposed approach relies on both the use of an augmented Lagrangian formulation and a price-decomposition-coordination algorithm. The state estimation of an openchannel hydraulic system ill...

The Signorini problem describes the contact of a linearly elastic body with a rigid frictionless foundation. It is transformed into a saddle point problem of some augmented Lagrangian functional and then discretized by nite element methods. Optimal error estimates are obtained for general smooth domains which are not necessarily convex. The key ingredient in the analysis is a discrete inf-sup c...

In this paper relationships between Pareto points and saddle points in multiple objective programming are investigated. Convex and nonconvex problems are considered and the equivalence between Pareto points and saddle points is proved in both cases. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. Partitions of the ind...

The numerical simulation of the interaction between a free surface flow and a moving obstacle is considered for the analysis of hydroplaning flows. A new augmented Lagrangian method, coupled to fictitious domains and penalty methods, is proposed for the simulation of multiphase flows. The augmented Lagrangian parameter is estimated by an automatic analysis of the discretization matrix resulting...

This paper introduces compressed eigenfunctions of the Laplace-Beltrami operator on 3D manifold surfaces. They constitute a novel functional basis, called the compressed manifold basis, where each function has local support. We derive an algorithm, based on the alternating direction method of multipliers (ADMM), to compute this basis on a given triangulated mesh. We show that compressed manifol...