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...

We consider the inclusion of commitment of thermal generation units in the optimal management of the Brazilian power system. By means of Lagrangian relaxation we decompose the problem and obtain a nondifferentiable dual function that is separable. We solve the dual problem with a bundle method. Our purpose is twofold: first, bundle methods are the methods of choice in nonsmooth optimization whe...

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...