In this paper, the problem of Magnetic Resonance (MR) image reconstruction from partial Fourier samples has been considered. To this aim, we leverage the evidence that MR images are sparser than their zero-filled reconstructed ones from incomplete Fourier samples. This information can be used to define an optimization problem which searches for the sparsest possible image conforming with the av...

In this paper, we propose combining augmented Lagrangian optimization with the dual decomposition method to obtain a fast algorithm for approximate MAP (maximum a posteriori) inference on factor graphs. We also show how the proposed algorithm can efficiently handle problems with (possibly global) structural constraints. The experimental results reported testify for the state-of-the-art performa...

Rare category analysis is of key importance both in theory and in practice. Previous research work focuses on supervised rare category analysis, such as rare category detection and rare category classification. In this paper, for the first time, we address the challenge of unsupervised rare category analysis, including feature selection and rare category selection. We propose to jointly deal wi...

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 presents novel convergence results for the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN) in the context of distributed convex optimization. It is shown that ALADIN converges for a large class of convex optimization problems from any starting point to minimizers without needing line-search or other globalization routines. Under additional regularity a...

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 consider the separable nonlinear and strictly convex single-commodity network flow problem (SSCNFP). We develop a computational scheme for generating a primal feasible solution from any Lagrangian dual vector; this is referred to as “early primal recovery”. It is motivated by the desire to obtain a primal feasible vector before convergence of a Lagrangian scheme; such a vector is not availab...

We study non-convex quadratic minimization problems under (possibly non-convex) quadratic and linear constraints, and characterize both Lagrangian and Semi-Lagrangian dual bounds in terms of conic optimization. While the Lagrangian dual is equivalent to the SDP relaxation (which has been known for quite a while, although the presented form, incorporating explicitly linear constraints, seems to ...

Local Convergence Analysis of Augmented Lagrangian Methods for Piecewise Linear-Quadratic Composite Optimization Problems

in recent years, in iran and other countries the power systems are going to move toward creating a competition structure for selling and buying electrical energy. these changes and the numerous advantages of dgs have made more incentives to use these kinds of generators than before. therefore, it is necessary to study all aspects of dgs, such as size selection and optimal placement and impact o...