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...

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...

Augmented Lagrangian Methods for p-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing Huibin Chang and Xue-Cheng Tai2,∗ 1 School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387; Department of Mathematics, East China Normal University, Shanghai 200241, China. 2 Department of Mathematics, University of Bergen, Johaness Brunsgate 12, Berg...

In this paper, we study the semidefinite inverse eigenvalue problem of reconstructing a real n-by-n matrix C such that it is nearest to the original pre-estimated real n-by-n matrix Co in the Frobenius norm and satisfies the measured partial eigendata, where the required matrix C should preserve the symmetry, positive semidefiniteness, and the prescribed entries of the preestimated matrix Co. W...

[1] M. Gallieri, J. M. Maciejowski “lasso MPC: Smart Regulation of OverActuated Systems”, to appear in ACC 2012. [2] M. Annergren, A. Hansson, B. Wahlberg “An ADMM Algorithm for Solving l1 Regularized MPC”, submitted. [3] S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers”, Foundations and Tr...

This note shows the O(1/t) convergence rate of Eckstein and Bertsekas’s generalized alternating direction method of multipliers in the context of convex minimization with linear constraints.

We compare three different time discretization schemes in combination with an augmented Lagrangian method to simulate the motion of an inextensible beam. The resulting saddle-point problem is solved with an Uzawa-DouglasRachford algorithm. The three schemes are tested on a benchmark with an analytical solution and on a more challenging application. We found that in order to obtain optimal conve...